Substitution of the phosphonamidate linkage (PO2-NH) for the peptide bond (CO-NH) in substrate-like sequences produces inhibitors of human skin fibroblast collagenase with Ki's far below Km for the native collagen substrate. Using a thiol ester substrate at pH 6.5, phthaloyl-GlyP-Ile-Trp-(S)NHCH-(Me)Ph, the phosphonamidate analog of phthaloyl-Gly-Ile-Trp-(S)NHCH(Me)Ph, has a Ki of 20 nM. Peptide phosphonamidates with amino acid sequences extended further to the right or the left of the Gly-Ile-Trp sequence had higher Ki's. Substitution of the phosphinate linkage (PO2-CH2) for the peptide bond also gives potent inhibitors such as napthoyl-GlyP-C-Leu-Trp-NHBzl, the phosphinate analog of naphtholyl-Gly-Leu-Trp-NHBzl, which has a Ki of 10 nM. Some of the phosphonamidates and phosphinates are also excellent inhibitors of the bacterial zinc metalloproteases thermolysin and Pseudomonas aeruginosa elastase.