The Pyrazolo[1,5-a]pyrimidine derivatives represented by formula I and their pharmaceutically acceptable salts exhibit excellent MAPKAP-K2 inhibiting activity. Drugs comprising the compounds as effective ingredients are therefore expected to be useful as therapeutic or prophylactic agents for MAPKAP-K2 mediated disorder, such as inflammatory disease, autoimmune disease, destructive bone disorder, cancer and/or tumour growth. ##STR00001##