Sulfonamide compounds are described which are inhibitors of matrix metalloproteinases, particularly stromelysin-1 and gelatinase A (72 kD gelatinase). Also described are methods for the treatment of multiple sclerosis, atherosclerotic plaque rupture, aortic aneurism, heart failure, restenosis, periodontal disease, corneal ulceration, burns, decubital ulcers, chronic ulcers or wounds, cancer metastasis, tumor angiogenesis, arthritis, or other autoimmune or inflammatory disorders dependent upon tissue invasion by leukocytes using the compounds.