A whitening-resistant, highly melt-viscoelastic ethylene-propylene copolymer and process for producing the same are provided, which copolymer is produced by copolymerizing ethylene with propylene in the presence of a specified stereoregular catalyst and at four stages under specified conditions, the catalyst being prepared by reacting an organoaluminum compound or its reaction product with an electron donor, with TiCl.sub.4, reacting the resulting solid product with an electron donor and an electron acceptor, and combining the resulting solid product with an organo-aluminum compound and an aromatic carboxylic acid ester so as to give a specified ratio, and at the four stages, the ethylene contents in monomers fed, the proportion of polymerization amounts and the intrinsic viscosities of polymers formed being specified.