To provide a thermoplastic elastomer composition having excellent fluidity and capable of preparing a molded product having excellent flexibility, heat and abrasion resistances, a high strength, a low hardness, rubber elasticity and processing stability or a molded product having the excellent flexibility, heat, abrasion and compression set resistances, high strength, low hardness, rubber elasticity and processing stability and a method for producing the composition.

This thermoplastic elastomer composition is obtained by feeding (A) an ethylene-unsaturated carboxylic acid copolymer or its ionomer, (B) a peroxide cross-linkable material and, as necessary, a mineral oil softener to an extruder and dynamically heat-treating the resultant material in the presence of a peroxide (C). The content of the unsaturated carboxylic acid of the copolymer is preferably 2-35 wt.%. The method for producing the thermoplastic elastomer composition is provided.