1. A process for preparing a 3-alkenylcephem compound or 3-norcephem compound of the formula (3) characterized in that an alkenyl halide of the formula (2), a nickel catalyst, a metal up to -0.3 (V/SCE) in standard oxidation reduction potential and a compound of a metal having a higher standard oxidation reduction potential than the metal are caused to act on a 3-cephem compound of the formula (1) in a solvent ##STR1## wherein R.sup.1 is a hydrogen atom or the like, R.sup.2 is a hydrogen atom or the like, R.sup.3 is a hydrogen atom or carboxylic acid protective group, and X is a halogen atom or the like, wherein R.sup.4 is 1-alkenyl having or not having a substituent, and Y is a halogen atom ##STR2## wherein R.sup.1, R.sup.2 and R.sup.3 are as defined above, and R.sup.5 is a hydrogen atom or 1-alkenyl having or not having a substituent.
