The invention provides pyrrolo[3,2-d]pyrimidine derivatives represented by formula (I), and their medically acceptable salts. The compounds of the invention exhibit GSK-3 inhibiting activity and are therefore expected to be useful as therapeutic or prophylactic agents for conditions in which GSK-3 is implicated, such as diabetes, diabetes complications, Alzheimer's disease, neurodegenerative diseases, manic depression, traumatic encephalopathy, alopecia, inflammatory diseases, cancer and immune deficiency. ##STR00001##