Abstract: Disclosed is a thermoplastic olefin polymer having elastic properties comprisinga) greater than 60 to 85 parts of a crystalline polymer fraction selected from the group consisting of (i) a copolymer of propylene and at least one alpha-olefin, (ii) a polybutene-1, (iii) an ethylene homopolymer or ethylene/alpha-olefin copolymer, (iv) polymer fraction (i), (ii) or (iii) in combination with, or mixtures thereof alone or in combination with, from 10 to 90 parts, based on the thermoplastic olefin polymer, of a homopolymer of propylene;b) from about 1 up to less than 15 parts of a semi-crystalline, low density, essentially linear copolymer fraction consisting substantially of units of the alpha-olefin used to prepare c) or the alpha-olefin used to prepare c) present in the greatest amount when two alpha-olefins are used; andc) from about 10 to less than 39 parts of an amorphous copolymer fraction of an alpha-olefin and propylene, with or without a diene or a different alpha-olefin termonomer.