A process for producing a polymer or copolymer of a norbornene derivative, which comprises contacting at a temperature in the range from -30.degree. to +200.degree. C in an inert atmosphere at least one norbornene derivative having at least one nitrile group, or a monomer mixture of at least one of said norbornene derivative and at least one cycloolefin other than cyclohexene, with a catalyst composition consisting essentially of a reaction mixture of (A) at least one member selected from the group consisting of halides, oxyhalides, alkoxyhalides and phenoxyhalides of W and Mo, (B) at least one member selected from the group consisting of organometallic compounds of elements of Groups IA, IIA, IIB and IIIA of the Deming Periodic Table, and (C) at least one member selected from the group consisting of oxides, hydroxides, nitrates, sulfates, phosphates, formates, acetates, acetylacetone complexes, alkoxides, alkenoxides, phenoxides and ammine complexes of V, Cr and Mn, oxides, sulfates, phosphates, alkoxides, alkenoxides, phenoxides, acetylacetone complexes, cyclopentadienyl complexes, hydride complexes and silicides of elements of Group IVB of the Deming Periodic Table and oxides, peroxides, hydroxides, sulfates, phosphates, formates, acetates, acetylacetone complexes, alkoxides, alkenoxides, phenoxides and ammine complexes of elements of Group VIII of the Deming Periodic Table;
- the metal atom ratio of the component (C) to the component (A) being 0.001 to 50, and the proportion of the component (B) being 1 to 10 moles per mole of the component (A).