Abstract: Polyolefin rubber which is an ethylene/propylene and/or 1-butene copolymer, which has a melt index of 0.3 to 15 dg/min and a relative density of 0.860 to 0.885, comprising 74-91 mol % of units derived from ethylene and 9-26 mol % of units derived from propylene and/or from 1-butene, characterised by a crystalline melting point J of 100.degree. to 125.degree. C. The process for obtaining this rubber consists in copolymerising, at a temperature of 150.degree.-300.degree. C. and at a pressure of 400-2000 bars, a gas stream containing 15-42% by vol. of ethylene and 58-85% by vol. of propylene and/or 1-butene, in the presence of a Ziegler-type catalyst system comprising at least one compound of a transition metal of groups IVB, VB, VIB and VIII of the Periodic Classification, and at least one organoaluminium compound and, if appropriate, in the presence of at least one chain transfer agent.