There are provided (I) a process for producing a copolymer of ethylene, an .alpha.-olefin having from 3 to 20 carbon atoms and optionally a polyene, which comprises the step of copolymerizing those monomers in a polymerization reactor by feeding the following components (A), (B), (C1) and (D) to the polymerization reactor: (A) a transition metal complex, (B) an organic aluminum compound, (C1) a halogen-containing compound, and (D) a Lewis base, wherein those components are fed to the polymerization reactor without a preliminary contact of (1) the component (A) with the component (B), (2) the component (A) with the component (C1), (3) the component (B) with the component (C1), and (4) the component (B) with the component (D); and (II) a process for producing said copolymer, which comprises the step of copolymerizing those monomers in a polymerization reactor (i) by feeding to the polymerization reactor the components (A), (B), (D), (C2) a halogen-containing compound, which is a derivative of an aryl group-containing carboxylic acid, and (C3) a halogen-containing compound, which is not a derivative of a carboxylic acid, or (ii) by feeding thereto the components (A), (B), (D), (C3), and (C4) a halogen-containing compound, which is a derivative of a carboxylic acid containing an unsaturated bond-carrying linear organic group.