A cyclo-olefinic random copolymer composed of an alpha-olefin component having 3 to 20 carbon atoms and a cyclo-olefin component,(i) said copolymer containing 5 to 99 mole % of recurring units derived from said alpha-olefin component having 3 to 20 carbon atoms and 1 to 95 mole % of recurring units derived from said cyclo-olefin component, and(ii) said copolymer having an intrinsic viscosity [.eta.], measured in decalin at 135.degree. C., of from 0.01 to 10 dl/g; and an olefinic random copolymer composed of (A) an olefin component having 3 to 20 carbon atoms and (B) a cyclic polyene component and as required, (C) a cyclo-olefin component,(i) said copolymer containing 5 to 99 mole % of recurring units derived from said alpha-olefin component (A) having 3 to 20 carbon atoms and 1 to 95 mole % of recurring units derived from said cyclic polyene component (B) and 0 to 90 mole % of recurring units derived from said cyclo-olefin component (C), and(ii) said copolymer having an intrinsic viscosity [.eta.], measured in decalin at 135.degree. C., of from 0.01 to 10 dl/g; and a process for production thereof. Also provided is a process for producing a cyclo-olefinic random copolymer, which comprises copolymerizing an alpha-olefin and a cyclo-olefin in the presence of a catalyst formed from(A) a compound of a transition metal of Group IVB of the periodic table having as a ligand a multidentate coordination compound in which at least two conjugated cycloalkadienyl groups or substituted products thereof are bonded via a lower alkylene group, and(B) an aluminoxane.