A family of molecules is disclosed that inhibit matrix metalloprotease (MMP) activity, and particularly inhibit the activity of one or more of MMP-2, MMP-9, or MMP-13, while generally exhibiting little activity against MMP-1. A contemplated compound also exhibits little inhibition of the production of TNF. A contemplated compound is an .alpha.-amino-.beta.-sulfonyl carbocyclo, heterocyclo, aryl, or heteroaryl hydroxamic acid. Also disclosed are processes for preparing a contemplated compound and for treating a mammal having a condition associated with pathological matrix metalloprotease activity.