The invention relates to a dihydrospiro-[cycloalkylamine]-pyrimidone derivative represented by formula (I) or a salt thereof: wherein: X represents two hydrogen atoms, a sulfur atom, an oxygen atom or a C.sub.1-2 alkyl group and a hydrogen atom; Y represents a bond, a carbonyl group, a methylene group optionally substituted; R1 represents a 2, 3 or 4-pyridine ring or a 2, 4 or 5-pyrimidine ring, the ring being optionally substituted; R2 represents a benzene ring or a naphthalene ring; the rings being optionally substituted; R3 represents a hydrogen atom, a C.sub.1-6 alkyl group or a halogen atom; R4 represents a hydrogen atom, a C.sub.1-4 alkoxy carbonyl group, a C.sub.1-5 alkyl group optionally substituted; o and m represent 1 to 2; n represents 0 to 3; p represents 0 to 2; and q represents 0 to 2. The invention relates also to 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 disease caused by abnormal activity of GSK3.beta., such as Alzheimer disease.