A sulfonyl aromatic or heteroaromatic ring hydroxamic acid compound that inter alia inhibits matrix metalloprotease activity is disclosed as are a treatment process that comprises administering a contemplated sulfonyl aromatic or heteroaromatic ring hydroxamic acid compound in a MMP enzyme-inhibiting effective amount to a host having a condition associated with pathological matrix metalloprotease activity. A contemplated compound corresponds in structure to the formula ##STR00001## wherein W and the R groups are defined elsewhere.