Lactams, in particular epsilon-caprolactam, are produced by the hydrolytic cyclization of aminonitriles, in particular 6-aminocapronitrile, in the vapor phase in a plurality of adiabatic fixed bed reaction zones arranged in succession wherein at least a portion of the heat of the exothermic reaction is removed between each of the successive reaction zones. Conducting the reaction in such a mannerrequires less capital for the reactor itself. It has also been found that the product exiting such a reaction system can be directly fed to a distillation unit without the need of additional cooling or storing.