To obtain cyclic olefinic copolymer compositions excellent in impact resistance, transparency and heat resistance by copolymerizing a cyclic olefin in the presence of a specific copolymer to form a polymer having specific properties.

A desired cyclic olefin copolymer composition can be obtained by copolymerizing, in the presence of (A) an aromatic ring-containing vinyl hydrocarbon/conjugated diene copolymer having an intrinsic viscosity (in decalin at 135°C) of 0.5-5.0 dl/g, at least one glass transition temperature by DSC of lower than 15°C and containing a polymerizable C-C double bond with a content of the double bond by iodine value of 2-150 (g iodine/100 g polymer) and having a refractive index (25°C) of 1.50-1.65 or a hydrogenated copolymer thereof, (B) a ≥2C α-olefin with (C) a cyclic olefin represented by formula I or formula II, and the composition has a content of component (A) of 1-40 wt.% and a difference in refractive index between component A and a copolymer to be obtained by copolymerizing component (B) with component (C) in the absence of component (A) being not greater than 0.015.