A method of producing a resin composition for a coated member, which resin composition comprises a polymer obtained by polymerization of a monomer having an ethylenically unsaturated bond and a thermoplastic elastomer, said method being characterized by comprising the steps of: adding, before or during said polymerization of said monomer having an ethylenically unsaturated bond, a phenolic antioxidant represented by the following Formula, that is masked with an organoaluminum compound, to at least one of a catalyst system, a polymerization system and a piping, and performing said polymerization such that said phenolic antioxidant is incorporated in an amount of 0.001 to 0.5 parts by mass with respect to a total of 100 parts by mass of said polymer obtained by said polymerization of said monomer having an ethylenically unsaturated bond and said thermoplastic elastomer; and melt-kneading said polymer obtained by said polymerization of said monomer having an ethylenically unsaturated bond with said thermoplastic elastomer: (wherein, R 1 and R 2 each independently represent a hydrogen atom, an alkyl group having 1 to 5 carbon atoms which is optionally branched or an arylalkyl group having 7 to 9 carbon atoms; and R represents an alkyl group having 1 to 30 carbon atoms which is optionally branched, an alkenyl group having 2 to 30 carbon atoms which is optionally branched, a cycloalkyl group having 3 to 12 carbon atoms which is optionally substituted or an aryl group having 6 to 18 carbon atoms which is optionally substituted); molding the composition from step B into an article; wherein, in said step, said polymer obtained by polymerization of said monomer having an ethylenically unsaturated bond and said thermoplastic elastomer are melt-kneaded at a mass ratio, said polymer obtained by polymerization of said monomer having an ethylenically unsaturated bond/said thermoplastic elastomer, of 2/1 to 4/1. adding, before or during said polymerization of said monomer having an ethylenically unsaturated bond, a phenolic antioxidant represented by the following Formula, that is masked with an organoaluminum compound, to at least one of a catalyst system, a polymerization system and a piping, and performing said polymerization such that said phenolic antioxidant is incorporated in an amount of 0.001 to 0.5 parts by mass with respect to a total of 100 parts by mass of said polymer obtained by said polymerization of said monomer having an ethylenically unsaturated bond and said thermoplastic elastomer; and melt-kneading said polymer obtained by said polymerization of said monomer having an ethylenically unsaturated bond with said thermoplastic elastomer: (wherein, R 1 and R 2 each independently represent a hydrogen atom, an alkyl group having 1 to 5 carbon atoms which is optionally branched or an arylalkyl group having 7 to 9 carbon atoms; and R represents an alkyl group having 1 to 30 carbon atoms which is optionally branched, an alkenyl group having 2 to 30 carbon atoms which is optionally branched, a cycloalkyl group having 3 to 12 carbon atoms which is optionally substituted or an aryl group having 6 to 18 carbon atoms which is optionally substituted); molding the composition from step B into an article;