Azaspiro compounds of the formula:
wherein R₁ and R₂ independently represent hydrgen, a hydrocarbon residue which may have a substituent, or an acyl group which may have a substituent; R₃ represents hydrogen or a hydrocarbon residue which may have a substituent; each of X₁ and X₂ is oxygen or sulfur; Y represents oxygen, sulfur or a group of the formula: -N(R₄)-, wherein R₄ represents hydrogen or a lower alkyl group; m represents 0 or 1; n represents 0 or 1, and its salt are novel compounds, possess excellent brain functionimproving action, and are of use as drugs for the prevention and therapy of senile dementia of Alzheimer type, vascular-type dementia and dementia derived from Alzheimer's disease, Pick's disease, Huntington's disease, Creutzfeldt-Jakob's disease, Parkinson's disease and spinocerebellar degeneration.