There are disclosed a resin composition which is excellent in rubber elasticity, oil maintainability and adhesivity to a metal, and comprises a thermoplastic elastomer composition comprising a (a1) hydrogenated block copolymer which is obtained by hydrogenating a block copolymer consisting essentially of a polymer block composed principally of a vinyl aromatic compound and a polymer block composed principally of a conjugated diene compound, which has a weight average molecular weight of at least 200,000, in which the polymer block composed principally of a vinyl aromatic compound is polystyrene, and in which the content by weight of the polystyrene moiety contained in the hydrogenated block copolymer is 20 to 40%; a (b1) non-aromatic rubber-softening agent having a kinematic viscosity at 40° C. of at least 300 mm2s−1; and a (c1) modified polyolefinic resin, the resin composition having a hardness according to JIS K6253 of at most 50 degrees and a compression set according to JIS K6262 of at most 50%; a composite molded body of a metal and the thermo-plastic elastomer composition such as a gasket integrated with a metallic sheet; and processes for producing the above products.