2-Pyridinyl-6,7,8,9-tetrahydropyrimido[1,2-A]pyrimidin-4-one and 7-pyridinyl-2,3-dihydoimidazo[1,2-A]pyrimidin-5(1H)one derivatives

Abstract

The invention relates to a pyrimidone derivative represented by formula (I) or a salt thereof: wherein: X represents hydrogen atoms, a sulphur atom, an oxygen atom or a C 1-2 alkyl group and a hydrogen atom; Y represents a bond, an ethenylene group, an ethynylene group, a 1,2-cyclopropylene, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfoxyde group, a carbonyl group, a nitrogen atom being optionally substituted; or a methylene group optionally substituted; R1 represents a 2, 3 or 4-pyridyl group optionally substituted by a C 3-6 cycloalkyl group a C 1-4 alkyl group, a C 1-4 alkoxy group, a benzyl group or a halogen atom; when Y represents a bond, a methylene group optionally substituted or a carbonyl group then R2 represents a C 1-6 alkyl group, a C 3-6 cycloalkyl group, a C 1-4 alkylthio group, a C 1-4 alkoxy group, a C 1-2 perhalogenated alkyl group, a C 1-3 halogenated alkyl group, a 5,6,7,8-tetrahydronaphthyl ring, a naphthyl ring, a phenylthio group, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; when Y represents an ethenylene group, an ethynylene group, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfoxyde group or a nitrogen atom being optionally substituted then R2 represents a C 1-6 alkyl group, a C 3-6 cycloalkyl group, a C 1-2 perhalogenated alkyl group, a C 1-3 halogenated alkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring. And a medicament comprising the said derivative or a salt thereof as an active ingredient which is used for preventive and/or therapeutic treatment of a neurodegenerative diseases caused by abnormal activity of GSK3β such as Alzheimer's disease.

1 - 12 . (canceled)  
   
   
       13 . A method for the treatment or prevention of a disease caused by abnormal GSK3β activity which comprises administering to a patient in need of such treatment or prevention an effective amount of a compound according to formula (I):  
     
       
         
         
             
             
         
       
       wherein:  
       X represents two hydrogen atoms, a sulphur atom, an oxygen atom or a C 1-2  alkyl group and a hydrogen atom;  
       Y represents a bond, an ethenylene group, an ethynylene group, a 1,2-cyclopropylene, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfinyl group, a carbonyl group, a nitrogen atom being optionally substituted by a C 1-6  alkyl group, a phenyl or a benzyl group; or a methylene group optionally substituted by one or two groups chosen from a C 1-6  alkyl group, a phenyl group, a hydroxyl group and a C 1-4  alkoxy group;  
       R1 represents a 2, 3 or 4-pyridyl group optionally substituted by a C 3-6  cycloalkyl group, a C 1-4  alkyl group, a C 1-4  alkoxy group, a benzyl group or a halogen atom; 
 when Y represents a bond, a 1,2-cyclopropylene, a methylene group optionally substituted or a carbonyl group then R2 represents a C 1-6  alkyl group, a C 3-6  cycloalkyl group, a C 1-4  alkylthio group, a C 1-4  alkoxy group, a C 1-2 perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a 5,6,7,8-tetrahydronaphthyl ring, a naphthyl ring, a phenylthio group, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; the benzyl group or the rings being optionally substituted by 1 to 4 substituents selected from a C 1-6  alkyl group, a methylendioxy group, a halogen atom, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a hydroxyl group, a C 1-4  alkoxy group, a nitro, a cyano, an amino, a C 1-5  monoalkylamino group, a C 2-10  dialkyl-amino group, a C 1-6  alkylcarbonylamino group, a C 6,10  arylcarbonylamino group, a C 1-4  alkyl-sulfonyl group, C 1-4  alkylsulfonyloxy group and a phenyl group;  
 when Y represents an ethenylene group, an ethynylene group, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfoxyde group or a nitrogen atom being optionally substituted then R2 represents a C 1-6  alkyl group, a C 3-6  cycloalkyl group, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; the benzyl group or the rings being optionally substituted by 1 to 4 substituents selected from a C 1-6  alkyl group, a methylendioxy group, a halogen atom, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a hydroxyl group, a C 1-4  alkoxy group, a nitro, a cyano, an amino, a C 1-5  monoalkylamino group, a C 2-10  dialkylamino group, a C 1-6  alkylcarbonylamino group, a C 6,10  arylcarbonylamino group, a C 1-4  alkylsulfonyl group, a C 1-4  alkylsulfonyloxy group and a phenyl group;  
 
       m represents 1 or 2;  
       and n represents 0 to 3; or a salt, solvate or hydrate thereof.  
     
   
   
       14 . A method according to  claim 13 , wherein in said compound of formula I, R1 represents an unsubstituted 4-pyridyl group.  
   
   
       15 . A method according to  claim 14 , wherein in said compound according to formula I, R2 represents a C 1-4  alkyl group, C 1-2  alkylthio group, C 1-2  alkoxy group, a trifluoromethyl group, a C 5-6  cycloalkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a phenyl ring, a pyridyl ring, an indole ring, a thiophene ring; the rings being optionally substituted by 1 to 4 substituents.  
   
   
       16 . A method according to  claim 13 , wherein said compound of formula I is selected from the group consisting of: 
 9-[2-(1H-indol-3-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenylethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(1H-indol-3-yl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenoxyethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-methylenedioxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-methoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-fluorophenoxyethyl)]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-chlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-methylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-trifluoromethylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(4-phenylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-methylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido [1,2-a]pyrimidin-4-one;    9-[2-(2,5-dimethoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-methoxyphenoxy)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1.2-a]pyrimidin-4-one;    9-[3-(2-methoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-chlorophenoxy)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3-methoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-methoxyphenylmethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-phenylthioethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-dimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4,5-trimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(phenylsulfonyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenylpropanoyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2,5-dimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2,4-dichlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3 -(4-chlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3,3-dimethylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-cyclohexylethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(pyridin-3-yl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylsulfonyloxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3,3-diphenylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[4-(4-methoxyphenyl)butyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[4-(4-nitrophenyl)butyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylprop-2-ynyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-chloro-4-fluorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-2-oxo-ethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-benzyloxypropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methylthiobutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(1-naphthyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(thiophen-2-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-trifluoromethylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[(2-(thiophen-3-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-bromophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido [1,2-a]pyrimidin-4-one;    9-(4-cyclohexylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-bromophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-ter-butylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2,4,6-trimethylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-ethoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-chloro-6-fluorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methoxybutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-cyclohexylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-[di(phenylmethyl)amino]propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-cyclopropylmethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylprop-2-enyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-2-hydroxypropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)-3-oxo-propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido [1,2-a]pyrimidin-4-one;    9-(4,4,4-trifluorobutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenyl-3-oxo-propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2 -a]pyrimidin-4-one;    9-[3-phenyl-3-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3,3,3-trifluoro-2-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    (R)-9-[2-phenyl-2-hydroxyethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    (S)-9-[2-phenyl-2-hydroxyethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)-3-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[1-methyl-2-oxo-2-phenyl-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[1-methyl-2-hydroxy-2-phenyl-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-chlorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-fluorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-phenylphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methoxyphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-naphthyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydronapht-2-yl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methoxy-4,5-methylendioxyphenyl)-2-oxo-1-methylethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1 ,2-a]pyrimidin-4-one;    9-[2-(4-methylphenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(1,1,4,4,-tetramethyl-1,2,3,4-tetrahydronapht-6-yl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(phenylamino)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-fluorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one; and    9-[2-(3-fluorophenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one; or a salt, solvate or hydrate thereof.    
   
   
       17 . A method according to  claim 13 , wherein said compound of formula I is selected from the group consisting of: 
 1-[2-(1H-Indol-3 -yl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(phenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(1H-indol-3-yl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-methylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-methoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4-phenylbutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-chlorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2,5-dimethoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-methylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3-methoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3,4,5-trimethoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-fluorophenoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-chlorophenoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2,4-dichlorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenylthio)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(3-phenylpropanoyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-fluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3,4-difluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-]pyrimidin-5(1H)-one,    1-(2-cyclohexylethyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(3,3-dimethylbutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(H)-one,    1-(2-phenyl-2-oxo-ethyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    (S)-1-(4,4,4-trifluoro-3-hydroxybutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4,4,4-trifluoro-but-2-en-1-yl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-trifluoromethylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    (R)-1-(4,4,4-trifluoro-3-hydroxybutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-fluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(2,5-dimethoxy-phenyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenylsulfonyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4,4,4-trifluorobutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(pyridin-3-yl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(2-methoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-chloro-phenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(napht-2-yl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(3-methoxy-4,5-methylendioxy-phenyl)-2-oxo-1-methyl-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-phenyl-phenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-methylphenyl)2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydronapht-2-yl)2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-fluorophenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one, and    1-[2-(3-methoxyphenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one; or a salt, solvate or hydrate thereof.    
   
   
       18 . A method for the treatment or prevention of a neurodegenerative disease which comprises administering to a patient in need of such treatment or prevention an effective amount of a compound according to formula (I):  
     
       
         
         
             
             
         
       
       wherein:  
       X represents two hydrogen atoms, a sulphur atom, an oxygen atom or a C 1-2  alkyl group and a hydrogen atom;  
       Y represents a bond, an ethenylene group, an ethynylene group, a 1,2-cyclopropylene, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfinyl group, a carbonyl group, a nitrogen atom being optionally substituted by a C 1-6  alkyl group, a phenyl or a benzyl group; or a methylene group optionally substituted by one or two groups chosen from a C 1-6  alkyl group, a phenyl group, a hydroxyl group and a C 1-4  alkoxy group;  
       R1 represents a 2, 3 or 4-pyridyl group optionally substituted by a C 3-6  cycloalkyl group, a C 1-4  alkyl group, a C 1-4  alkoxy group, a benzyl group or a halogen atom; 
 when Y represents a bond, a 1,2-cyclopropylene, a methylene group optionally substituted or a carbonyl group then R2 represents a C 1-6  alkyl group, a C 3-6  cycloalkyl group, a C 1-4  alkylthio group, a C 1-4  alkoxy group, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a 5,6,7,8-tetrahydronaphthyl ring, a naphthyl ring, a phenylthio group, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; the benzyl group or the rings being optionally substituted by 1 to 4 substituents selected from a C 1-6  alkyl group, a methylendioxy group, a halogen atom, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a hydroxyl group, a C 1-4  alkoxy group, a nitro, a cyano, an amino, a C 1-5  monoalkylamino group, a C 2-10  dialkyl-amino group, a C 1-6  alkylcarbonylamino group, a C 6,10  arylcarbonylamino group, a C 1-4  alkyl-sulfonyl group, C 1-4  alkylsulfonyloxy group and a phenyl group;  
 when Y represents an ethenylene group, an ethynylene group, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfoxyde group or a nitrogen atom being optionally substituted then R2 represents a C 1-6  alkyl group, a C 3-6  cycloalkyl group, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; the benzyl group or the rings being optionally substituted by 1 to 4 substituents selected from a C 1-6  alkyl group, a methylendioxy group, a halogen atom, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a hydroxyl group, a C 1-4  alkoxy group, a nitro, a cyano, an amino, a C 1-5  monoalkylamino group, a C 2-10  dialkylamino group, a C 1-6  alkylcarbonylamino group, a C 6,10  arylcarbonylamino group, a C 1-4  alkylsulfonyl group, a C 1-4  alkylsulfonyloxy group and a phenyl group;  
 
       m represents 1 or 2;  
       and n represents 0 to 3; or a salt, solvate or hydrate thereof.  
     
   
   
       19 . A method according to  claim 18 , wherein in said compound of formula I, R1 represents an unsubstituted 4-pyridyl group.  
   
   
       20 . A method according to  claim 19 , wherein in said compound according to formula I, R2 represents a C 1-4  alkyl group, C 1-2  alkylthio group, C 1-2  alkoxy group, a trifluoromethyl group, a C 5-6  cycloalkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a phenyl ring, a pyridyl ring, an indole ring, a thiophene ring; the rings being optionally substituted by 1 to 4 substituents.  
   
   
       21 . A method according to  claim 18 , wherein said compound of formula I is selected from the group consisting of: 
 9-[2-(1H-indol-3-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenylethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(1H-indol-3-yl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenoxyethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-methylenedioxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-methoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-fluorophenoxyethyl)]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-chlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-methylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-trifluoromethylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(4-phenylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-methylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2,5-dimethoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-methoxyphenoxy)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-methoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[2-a]pyrimidin-4-one;    9-[2-(4-chlorophenoxy)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3 -(3-methoxyphenyl)propyl-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-methoxyphenylmethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-phenylthioethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-dimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido1,2-a]pyrimidin-4-one;    9-[3-(3,4,5-trimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(phenylsulfonyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenylpropanoyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2,5-dimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2,4-dichlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-chlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3,3-dimethylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-cyclohexylethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(pyridin-3-yl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylsulfonyloxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3,3-diphenylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[4-(4-methoxyphenyl)butyl]-2-pyridin-4-yi-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[(4-nitrophenyl)butyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylprop-2-ynyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-chloro-4-fluorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-2-oxo-ethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-benzyloxypropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methylthiobutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(1-naphthyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(thiophen-2-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-trifluoromethylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[(2-(thiophen-3-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-bromophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido [1,2-a]pyrimidin-4-one;    9-(4-cyclohexylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-bromophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-ter-butylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2,4,6-trimethylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-ethoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-chloro-6-fluorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methoxybutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-cyclohexylpropyl)-2-pyridin-4- yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-[di(phenylmethyl)amino]propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-cyclopropylmethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylprop-2-enyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-2-hydroxypropyl)-2-pyridin-4-yn-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)-3-oxo-propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(4,4,4-trifluorobutyl)-2-pyridin-4-yn-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenyl-3-oxo-propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenyl-3-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3,3,3-trifluoro-2-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    (R)-9-[2-phenyl-2-hydroxyethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    (S)-9-[2-phenyl-2-hydroxyethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)-3-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[1-methyl-2-oxo-2-phenyl-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[1-methyl-2-hydroxy-2-phenyl-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-chlorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-fluorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-phenylphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methoxyphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-naphthyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydronapht-2-yl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methoxy-4,5-methylendioxyphenyl)-2-oxo-1-methylethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylphenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(1,1,4,4,-tetramethyl-1,2,3,4-tetrahydronapht-6-yl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(phenylamino)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido [1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-fluorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one; and    9-[2-(3-fluorophenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one; or a salt, solvate or hydrate thereof.    
   
   
       22 . A method according to  claim 18 , wherein said compound of formula I is selected from the group consisting of: 
 1-[2-(1H-Indol-3-yl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(phenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(1H-indol-3-yl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-methylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-methoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5( 1H)-one,    1-(4-phenylbutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-chlorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2,5-dimethoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-methylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3-methoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3,4,5-trimethoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-fluorophenoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-chlorophenoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2,4-dichlorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenylthio)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(3-phenylpropanoyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-fluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3,4-difluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo [1,2-a]pyrimidin-5(1H)-one,    1-(2-cyclohexylethyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(3,3-dimethylbutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(2-phenyl-2-oxo-ethyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    (S)-1-(4,4,4-trifluoro-3-hydroxybutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4,4,4-trifluoro-but-2-en-1-yl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-trifluoromethylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    (R)-1-(4,4,4-trifluoro-3-hydroxybutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-fluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(2,5-dimethoxy-phenyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenylsulfonyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5( 1H)-one,    1-(4,4,4-trifluorobutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(pyridin-3-yl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(2-methoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-chloro-phenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(napht-2-yl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(3-methoxy-4,5-methylendioxy-phenyl)-2-oxo-1-methyl-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-phenyl-phenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-methylphenyl)2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydronapht-2-yl)2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-fluorophenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one, and    1-[2-(3-methoxyphenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one; or a salt, solvate or hydrate thereof.    
   
   
       23 . A method according to  claim 18  wherein said neurodegenerative disease is selected from the group consisting of Alzheimer's disease, Parkinson's disease, tauopathies, vascular dementia, acute stroke, traumatic injuries, cerebrovascular accidents, brain cord trauma, spinal cord trauma, peripheral neuropathies, retinopathies and glaucoma.  
   
   
       24 . A method according to  claim 19  wherein said neurodegenerative disease is selected from the group consisting of Alzheimer's disease, Parkinson's disease, tauopathies, vascular dementia, acute stroke, traumatic injuries, cerebrovascular accidents, brain cord trauma, spinal cord trauma, peripheral neuropathies, retinopathies and glaucoma.  
   
   
       25 . A method according to  claim 20  wherein said neurodegenerative disease is selected from the group consisting of Alzheimer's disease, Parkinson's disease, tauopathies, vascular dementia, acute stroke, traumatic injuries, cerebrovascular accidents, brain cord trauma, spinal cord trauma, peripheral neuropathies, retinopathies and glaucoma.  
   
   
       26 . A method according to  claim 21  wherein said neurodegenerative disease is selected from the group consisting of Alzheimer's disease, Parkinson's disease, tauopathies, vascular dementia, acute stroke, traumatic injuries, cerebrovascular accidents, brain cord trauma, spinal cord trauma, peripheral neuropathies, retinopathies and glaucoma.  
   
   
       27 . A method according to  claim 22  wherein said neurodegenerative disease is selected from the group consisting of Alzheimer's disease, Parkinson's disease, tauopathies, vascular dementia, acute stroke, traumatic injuries, cerebrovascular accidents, brain cord trauma, spinal cord trauma, peripheral neuropathies, retinopathies and glaucoma.  
   
   
       28 . A method for the treatment or prevention of obesity, manic depressive illness, schizophrenia, alopecia or cancers which comprises administering to a patient in need of such treatment or prevention an effective amount of a compound according to formula (I):  
     
       
         
         
             
             
         
       
       wherein:  
       X represents two hydrogen atoms, a sulphur atom, an oxygen atom or a C 1-2  alkyl group and a hydrogen atom;  
       Y represents a bond, an ethenylene group, an ethynylene group, a 1,2-cyclopropylene, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfinyl group, a carbonyl group, a nitrogen atom being optionally substituted by a C 1-6  alkyl group, a phenyl or a benzyl group; or a methylene group optionally substituted by one or two groups chosen from a C 1-6  alkyl group, a phenyl group, a hydroxyl group and a C 1-4  alkoxy group;  
       R1 represents a 2, 3 or 4-pyridyl group optionally substituted by a C 3-6  cycloalkyl group, a C 1-4  alkyl group, a C 1-4  alkoxy group, a benzyl group or a halogen atom; 
 when Y represents a bond, a 1,2-cyclopropylene, a methylene group optionally substituted or a carbonyl group then R2 represents a C 1-6  alkyl group, a C 3-6  cycloalkyl group, a C 1-4  alkylthio group, a C 1-4  alkoxy group, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a 5,6,7,8-tetrahydronaphthyl ring, a naphthyl ring, a phenylthio group, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; the benzyl group or the rings being optionally substituted by 1 to 4 substituents selected from a C 1-6  alkyl group, a methylendioxy group, a halogen atom, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a hydroxyl group, a C 1-4  alkoxy group, a nitro, a cyano, an amino, a C 1-5  monoalkylamino group, a C 2-10  dialkyl-amino group, a C 1-6  alkylcarbonylamino group, a C 6,10  arylcarbonylamino group, a C 1-4  alkyl-sulfonyl group, C 1-4  alkylsulfonyloxy group and a phenyl group;  
 when Y represents an ethenylene group, an ethynylene group, an oxygen atom, a sulphur atom, a sulfonyl group, a sulfoxyde group or a nitrogen atom being optionally substituted then R2 represents a C 1-6  alkyl group, a C 3-6  cycloalkyl group, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a benzyl group, a phenyl ring, a pyridyl ring, an indole ring, a pyrrole ring, a thiophene ring, a furan ring or an imidazole ring; the benzyl group or the rings being optionally substituted by 1 to 4 substituents selected from a C 1-6  alkyl group, a methylendioxy group, a halogen atom, a C 1-2  perhalogenated alkyl group, a C 1-3  halogenated alkyl group, a hydroxyl group, a C 1-4  alkoxy group, a nitro, a cyano, an amino, a C 1-5  monoalkylamino group, a C 2-10  dialkylamino group, a C 1-6  alkylcarbonylamino group, a C 6,10  arylcarbonylamino group, a C 14  alkylsulfonyl group, a C 1-4  alkylsulfonyloxy group and a phenyl group;  
 
       m represents 1 or 2;  
       and n represents 0 to 3; or a salt, solvate or hydrate thereof.  
     
   
   
       29 . A method according to  claim 28 , wherein in said compound of formula I, R1 represents an unsubstituted 4-pyridyl group.  
   
   
       30 . A method according to  claim 29 , wherein in said compound according to formula I, R2 represents a C 1-4  alkyl group, C 1-2  alkylthio group, C 1-2  alkoxy group, a trifluoromethyl group, a C 5-6  cycloalkyl group, a naphthyl ring, a 5,6,7,8-tetrahydronaphthyl ring, a phenyl ring, a pyridyl ring, an indole ring, a thiophene ring; the rings being optionally substituted by 1 to 4 substituents.  
   
   
       31 . A method according to  claim 28 , wherein said compound of formula I is selected from the group consisting of: 
 9-[2-(1H-indol-3-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenylethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(1H-indol-3-yl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenoxyethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-methylenedioxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-methoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-fluorophenoxyethyl)]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-chlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-methylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-trifluoromethylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(4-phenylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-methylphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido [1,2-a]pyrimidin-4-one;    9-[2-(2,5-dimethoxyphenyl)ethyl]-2-pyridin-4-y1-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-methoxyphenoxy)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-methoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-chlorophenoxy)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3-methoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-methoxyphenylmethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-phenylthioethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-dimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4,5-trimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(phenylsulfonyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3,4-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenylpropanoyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2,5-dimethoxyphenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2,4-dichlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(3-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-chlorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3,3-dimethylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-cyclohexylethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(pyridin-3-yl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylsulfonyloxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3,3-diphenylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[4-(4-methoxyphenyl)butyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[4-(4-nitrophenyl)butyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(2-fluorophenyl)propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylprop-2-ynyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-chloro-4-fluorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-2-oxo-ethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-benzyloxypropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methylthiobutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-naphthyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(thiophen-2-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-trifluoromethylphenyl)ethyl]-2-pyridin-4-y-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[(2-(thiophen-3-yl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-bromophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(4-cyclohexylbutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-bromophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-ter-butylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2,4,6-trimethylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-ethoxyphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-chloro-6-fluorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methylphenyl)ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-methoxybutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-cyclohexylpropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-[di(phenylmethyl)amino]propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-cyclopropylmethyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(3-phenylprop-2-enyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(2-phenyl-2-hydroxypropyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)-3-oxo-propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-(4,4,4-trifluorobutyl)-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenyl-3-oxo-propyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-phenyl-3-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3,3,3-trifluoro-2-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    (R)-9-[2-phenyl-2-hydroxyethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    (S)-9-[2-phenyl-2-hydroxyethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[3-(4-fluorophenyl)-3-hydroxypropyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[1-methyl-2-oxo-2-phenyl-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[1-methyl-2-hydroxy-2-phenyl-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-chlorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-fluorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-phenylphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-methoxyphenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(2-naphthyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydronapht-2-yl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1 ,2-a]pyrimidin-4-one;    9-[2-(3-methoxy-4,5-methylendioxyphenyl)-2-oxo-1-methylethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(4-methylphenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(1,1,4,4,-tetramethyl-1,2,3,4-tetrahydronapht-6-yl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(phenylamino)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-chlorophenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one;    9-[2-(3-fluorophenyl)-2-oxo-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one; and    9-[2-(3-fluorophenyl)-2-hydroxy-ethyl]-2-pyridin-4-yl-6,7,8,9-tetrahydro-4H-pyrimido[1,2-a]pyrimidin-4-one; or a salt, solvate or hydrate thereof.    
   
   
       32 . A method according to  claim 28 , wherein said compound of formula I is selected from the group consisting of: 
 1-[2-(1H-Indol-3-yl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(phenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(1H-indol-3-yl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-methylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-methoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4-phenylbutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-chlorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2,5-dimethoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-methylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3-methoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3,4,5-trimethoxyphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-fluorophenoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-chlorophenoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2,4-dichlorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenylthio)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(3-phenylpropanoyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-fluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(3,4-difluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(2-cyclohexylethyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(3,3-dimethylbutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(2-phenyl-2-oxo-ethyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    (S)-1-(4,4,4-trifluoro-3-hydroxybutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4,4,4-trifluoro-but-2-en-1-yl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(4-trifluoromethylphenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    (R)-1-(4,4,4-trifluoro-3-hydroxybutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(2-fluorophenyl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(2,5-dimethoxy-phenyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(phenysulfonyl)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-(4,4,4-trifluorobutyl)-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[3-(pyridin-3-yl)propyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(2-methoxy)ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-chloro-phenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(napht-2-yl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(3-methoxy-4,5-methylendioxy-phenyl)-2-oxo-1-methyl-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-phenyl-phenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-methylphenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydronapht-2-yl)2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one,    1-[2-(4-fluorophenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one, and    1-[2-(3-methoxyphenyl)-2-oxo-ethyl]-7-pyridin-4-yl-2,3-dihydroimidazo[1,2-a]pyrimidin-5(1H)-one; or a salt, solvate or hydrate thereof.    
   
   
       33 . A method according to  claim 28  wherein said cancer is breast cancer, non-small cell lung carcinoma, thyroid cancer, T or B-cell leukemia or virus-induced tumors.  
   
   
       34 . A method according to  claim 29  wherein said cancer is breast cancer, non-small cell lung carcinoma, thyroid cancer, T or B-cell leukemia or virus-induced tumors.  
   
   
       35 . A method according to  claim 30  wherein said cancer is breast cancer, non-small cell lung carcinoma, thyroid cancer, T or B-cell leukemia or virus-induced tumors.  
   
   
       36 . A method according to  claim 31  wherein said cancer is breast cancer, non-small cell lung carcinoma, thyroid cancer, T or B-cell leukemia or virus-induced tumors.  
   
   
       37 . A method according to  claim 32  wherein said cancer is breast cancer, non-small cell lung carcinoma, thyroid cancer, T or B-cell leukemia or virus-induced tumors.