Monocyclic .beta.-lactam compounds represented by the formula ##STR1## wherein R.sub.1 is H, NH.sub.2, acylamino, C.sub.1 -C.sub.4 alkyl, etc.; R.sub.2 is e.g. C.sub.1 -C.sub.4 alkyl, hydroxyalkyl, aminoalkyl, carboxy, esterified carboxy, esterified carboxyalkyl, or carboxyalkyl; and R.sub.3 is hydrogen, benzyl, substituted benzyl, pivaloyl, --SO.sub.3 M, or --P(C.dbd.O)(OM')2; are obtained by the cyclization of an O-substituted hydroxamate of a .beta.-substituted alkylcarboxylic acid. For example, .alpha.-ethylmalic acid monobenzyl ester is reacted with O-benzylhydroxylamine to form the O-benzylhydroxamate of the free carboxy group, and the hydroxamate is cyclized with diethyl diazodicarboxylate and triphenylphosphine to form the .beta.-lactam of the above formula wherein R.sub.1 is ethyl, R.sub.2 is benzyloxycarbonyl and R.sub.3 is benzyl. The .beta.-lactam compounds are useful intermediates for preparing .beta.-lactamase inhibitors and monocyclic .beta.-lactam antibiotics and, when R.sub.3 is --SO.sub.3 M or --P(C.dbd.O)(OM')2 the compounds and salts thereof are antibacterial agents.