Novel 6-substituted amino-4-oxa-1-azabicyclo�3,2,0!heptan-7-one compounds, as well as the pharmaceutically acceptable salts thereof and diastereoisomers thereof, of formula I, ##STR1## are disclosed, which exhibit excellent cysteine protease inhibitory activity and may be used for treatment of different diseases such as muscular dystrophy, arthritis, myocardial infarction, Alzheimer's disease, bacterial infection, common cold, osteroporosis and cancer metastasis.