NOVELTY - A thermoplastic-elastomer composition comprises ethylene- alpha -olefin-nonconjugated polyene copolymer (A), alpha -olefin-type thermoplastic resin (B) having heat of fusion of 75 J/g or more, alpha -olefin-type resin (C) having heat of fusion of 15 J/g or less and crosslinking agent (D). The thermoplastic-elastomer composition is manufactured from raw material composition containing a sea island structure including a sea phase which contains the alpha -olefin-type thermoplastic resin (B) and an island phase containing ethylene- alpha -olefin and nonconjugated polyolefin copolymer (A).    USE - Thermoplastic-elastomer composition is used for forming molded product for composite component and manufacture of thermoplastic elastomer (all claimed) for weather strip of motor vehicles. Uses include but are not limited to gasket for window sealing and door sealing and trunk sealing, roof side rail, inner panel, door trim, console box, fuel cell stack, track pad for railways,, electric wire, medical device component, roll for information machines, skin material for ships and boats, etc.    ADVANTAGE - The composition has excellent adhesiveness with respect to vulcanized rubber. The molded product formed using the composition has excellent external appearance and improved hardness, and is manufactured without flow mark in molded component with shortened molding cycle.    DETAILED DESCRIPTION - A thermoplastic-elastomer composition comprises ethylene- alpha -olefin-nonconjugated polyene copolymer (A), alpha -olefin-type thermoplastic resin (B) having melting point of 140 degrees C or more and heat of fusion of 75 J/g or more measured based on JIS K 7122, alpha -olefin-type resin (C) having heat of fusion of 15 J/g or less measured based on JIS K 7122, and crosslinking agent (D). The thermoplastic-elastomer composition is manufactured from raw material composition containing a sea island structure including a sea phase which contains the alpha -olefin-type thermoplastic resin (B) and an island phase containing ethylene- alpha -olefin and nonconjugated polyolefin copolymer (A). INDEPENDENT CLAIMS are included for the following:    (1) composite component, which is obtained by joining thermoplastic-elastomer molded product obtained by molding the thermoplastic-elastomer composition and vulcanized rubber; and    (2) manufacture of thermoplastic elastomer, which involves heat-processing the thermoplastic-elastomer composition.