Abstract: An olefinic thermoplastic elastomer composition which does not exhibit problems due to a softening agent such as an oil is superior in molding processability. The thermoplastic elastomer composition is produced by a heat crosslinking process of a resin-rubber composition that contains an olefinic and/or diene rubber, an olefinic resin, and a vinyl copolymer. The vinyl copolymer is obtained by copolymerizing 20 wt % or more of a vinyl monomer represented by CH2═CHOCOR1 or CH2═CHOR2 wherein R1 and R2 are alkyl groups having 1-6 carbon atoms. The thermoplastic elastomer composition can include a vinyl copolymer that has not undergone a heat crosslinking process.