Provided are a thermoplastic resin composition which is excellent in oil resistance, heat resistance, weatherability, impact resistance, transparency, and moldability, and which can be produced economically, an elastomer composition with low hardness and high tensile strength which is excellent in oil resistance and compression set, and a molded object produced by molding the thermoplastic resin composition or elastomer composition. The composition is produced by compounding a thermoplastic resin or an elastomer with a block copolymer having at least one methacrylic ester polymer block and at least one acrylic ester polymer block. Also provided are a process for producing a methacrylic ester-acrylic ester-methacrylic ester block copolymer which requires hardly any purification, which is excellent in heat resistance and weatherability, and in which the molecular weight and the molecular-weight distribution are controlled, and a methacrylic ester-acrylic ester-methacrylic ester block copolymer produced by the process.