An object of the present invention is to provide an olefin-based thermoplastic elastomer composition that has both weatherability and flexibility at low temperatures, is excellent in fluidity, and causes no stickiness even in the use at high temperatures; a process oil composition for elastomers that serves as the raw material of the thermoplastic elastomer composition and contributes to the above characteristics; and an oil-extended elastomer containing the process oil composition.;The process oil composition for elastomers of the present invention has a property that, when 20 parts by weight of the process oil composition for elastomers are blended with respect to 100 parts by weight of a propylene homopolymer, the melting point of the propylene homopolymer is lowered by 2 to 4.5° C. compared to that of the propylene homopolymer without blending. The process oil composition for elastomers is a mixture of a purified mineral oil and a synthetic oil obtained by polymerizing (an) olefinic monomer(s), wherein the ratio of the purified mineral oil to the synthetic oil is preferably 40/60 to 80/20.
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