A propylene polymer composition is prepared by mixing propylene homo- or co-polymer (A) obtained using a transition metal catalyst compound (h), defined herein, with a co-catalyst, e.g., organoaluminum oxy compound, with an olefin elastomer (D) and another olefin polymer (E), e.g., polyethylene. Alternatively, the combination of propylene polymer (A), olefin elastomer (D) and olefin polymer (E) is prepared by a multi-stage polymerization method. In both cases, the propylene homo- or co-polymer (A) may include a second propylene homo- or co-polymer (A) wherein the ratio of intrinsic viscosities of propylene polymers (A) and (A) is in the range of 3 to 30. These propylene polymer compositions are excellent in heat resistance, mechanical strength, tensile elongation at break, etc., and can be used in the fabrication of structural materials, films and sheets.