A process for the preparation of 3-alkenylcephem or 3-norcephem compounds represented by general formula (3), characterized by treating a 3-cephem compound of general formula (1) in a solvent with an alkenyl halide of general formula (2), a nickel catalyst, a metal having a standard redox potential of -0.3 (V/SCE) or below , and a compound of a metal having a standard redox potential higher than that of the above metal. Formula (1) (wherein R1 is hydrogen or the like; R2 is hydrogen or the like; R3 is hydrogen or a carboxyl-protecting group; and X is halogeno or the like). (Formula 2) R4-Y wherein R4 is optionally substituted 1-alkenyl; and Y is halogeno. Formula (3) (wherein R?1, R2, and R3¿ are each as defined above; and R5 is hydrogen or optionally substituted 1-alkenyl).