Abstract: A rubbery copolymer of ethylene, an .alpha.-olefin having 3 to 10 carbon atoms and a polyene, characterized by having (A) an ethylene/.alpha.-olefin mole ratio of from 50/50 to 95/5, (B) an iodine value of from 5 to 50, (C) an intrinsic viscosity [.eta.], measured in decaline at 135.degree. C., of from 1.0 to 6.0 dl/g, (D) a weight average molecular weight/number average molecular weight ratio (Mw/Mn) of from 3 to 15, and (E) an iodine value index .alpha..sub.1 for the lower molecular weight components and an iodine value index .alpha..sub.2 for the higher molecular weight components, said .alpha..sub.1 and .alpha..sub.2 falling within the ranges -30.ltoreq..alpha..sub.1 .ltoreq.0 and 0<.alpha..sub.2 .ltoreq.30. Said copolymer can be obtained by copolymerizing ethylene, the .alpha.-olefin having 3 to 10 carbon atoms and polyene at a temperature of from about 40.degree. C. to about 100.degree. C. in the presence of a catalyst composed of (a) a vanadium compound of the formula VO(OR).sub.n X.sub.