The invention relates to a dihydrospiro-[cycloalkyl]-pyrimidone derivative represented by formula (I) or a salt thereof: ##STR00001## wherein X, Y, R1, R2, R3, m, n, p and q are as described herein. 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.