Thermoplastic elastomer composition excellent in heat bondability

A thermoplastic elastomer composition comprising a blend comprising (a) 10 to 100 parts by weight of a peroxide-crosslinking olefin copolymer rubber, (b) 0 to 90 parts by weight of an olefinic plastic, the sum of the amounts of the components (a) and (b) being 100 parts by weight, and (c) 0.01 to 10 parts by weight of an unsaturated epoxy monomer selected from the group consisting of a glycidyl ester of an unsaturated monocarboxylic acid, a diglycidyl ester of an unsaturated polycarboxylic acid, an unsaturated glycidyl ether, 2-(o-vinylphenyl)-ethylene oxide, 2-(p-vinylphenyl)-ethylene oxide, 2-(o-vinylphenyl)-propylene oxide, 2-(p-vinylphenyl)-propylene oxide, 2-(o-allylphenyl)-ethylene oxide, 2-(p-allylphenyl)-ethylene oxide, 2-(o-allylphenyl)-propylene oxide, 2-(p-allylphenyl)-propylene oxide, p-glycidylstyrene, 3,4-epoxy-1-butene, 3,4-epoxy-3-methyl-1-butene, 3,4-epoxy-1-pentene, 3,4-epoxy-3-methyl-1-pentene, 5,6-epoxy-1-hexene, vinylcyclohexene mono-oxide and allyl 3,3-epoxycyclopentyl ether, said thermoplastic elastomer composition being partially crosslinked by dynamically heat-treating said blend in the presence of an organic peroxide.