4-Cyano-2-azetidinone derivatives represented by the formula ##STR1## wherein R.sup.1 is an amino group which may be acylated or protected, X is a hydrogen atom or a methoxy group and W is a hydrogen atom or a sulfo group, and methods of producing the same, for example, as represented by ##STR2## wherein R.sup.2 is an acylated or protected amino group, Y is a halogen atom or a group having the formula --OCOR.sup.3, --SCOR.sup.3 or --S(O).sub.n --R.sup.3 (R.sup.3 being a hydrocarbyl group and n an integer 1 or 2), R.sup.4 is an amino group which may be acylated or protected and X is as defined above. Compounds [I] are useful as advantageous intermediates for the synthesis of optically active 4-substituted-2-azetidinone derivatives, and, when W=SO.sub.3 H, [I] are also useful as antimicrobial agents and as beta-lactamase inhibitors.