A class of catalysts for the anionic copolymerization of cyclic lactams in the presence of .omega.-(N-acyllactam)polyorganosiloxanes, .alpha.,.omega.-di-(N-acyllactam)polyorganosiloxanes or star-shaped .omega.-(N-acyllactam)polyorganosiloxanes is disclosed. The catalysts successfully protect the siloxane prepolymer from harmful depolymerization reactions at elevated temperatures while anionically polymerizing the cyclic lactams via ring-opening. Diblock, triblock, multiblock and star-block copolymers, e.g., of a polyorganosiloxane and a polyamide, with advantageously high polyorganosiloxane and polyamide block molecular weights and superior heat resistance can be synthesized with the catalysts. The composition of these block copolymers, with the structure AB, ABA, and star-(BA).sub.r, r .gtoreq.3, where A=polyamide and B=polyorganosiloxane, and the process for producing them are also described.