To economically produce the objective compound by a method of a two step process comprising a reaction of 4-chloro-butyroyl chloride with N-bromosuccinimide and further the reaction of the product with an amine.

A reaction of 4-Chloro-butyroyl chloride with N- bromosuccinimide is carried out by adding thionyl chloride at first and immediately adding a catalytic amount of hydrogen bromide thereto to provide a compound of formula I. Further, the compound of formula I is reacted with an amine of the formula, R-NH2 (R is H, a lower alkyl, a lower alkoxy, a cycloalkyl, a lower alkenyl, an aryl, a heterocycle, etc.) in non-aqueous medium in the presence of sodium hydroxide or potassium hydroxide, and a phase transfer catalyst to provide a compound of formula II in the method for producing an α-bromolactam derivative. The compound of formula II is useful for production of cephalosporins, cephem, carbacephem or an iso-oxacephem derivative. The method can shorten the processes, and provide the objective compound at a low cost without requiring a reagent causing trouble such as bromine atom.