Olefin thermoplastic elastomer composition and process for producing the same

A process for producing an olefin thermoplastic elastomer composition consisting essentially of the following components (A) and (B), said composition obtainable by first polymerizing a monomer of the component (A) and then polymerizing monomers of the component (B), said composition having Such fractionation properties that, in temperature rising elution fractionation in the temperature range of 0 to 140° C. using o-dichlorobenzene as a solvent, the eluate obtained at 0° C. is 35 to 60% by weight based on the total elution weight and the eluate obtained at 80 to 100° C. is 1 to 5% by weight based on the total elution weight:

• (A) 30 to 60% by weight, based on the whole composition, of a propylene homopolymer having an isotactic index of not less than 90%;
• and
• (B) 40 to 70% by weight, based on the whole composition, of a copolymer of propylene with other α-olefin having 2 to 8 carbon atoms, said copolymer comprising propylene and ethylene,
• said process comprising the steps of:
• polymerizing a monomer of the component (A) in the presence of a catalyst comprising an organoaluminum compound and a solid component, said solid component comprising a titanium atom, a magnesium atom, a halogen atom, and an electron-donating compound;
• and
• then polymerizing monomers of the component (B) in the presence of said catalyst.