To provide an industrial and highly active catalytic system easily obtained for copolymerization between an α-olefin and a cyclic olefin, and to provide a method for producing the copolymer by use of the catalytic system.

This copolymerization catalytic system is obtained by combining a metal complex having one molecule of a ligand including a cyclopentadienyl skeleton of a specific structure and a specific monovalent bidentate chelate anionic ligand with an activator having a specific structure. The alternative method for producing a copolymer using the catalytic system is provided.