A composition having excellent transparency, flexibility, rubber elasticity, thermal resistance, impact resistance, abrasion resistance and the like, a composition having excellent rigidity and impact resistance as well as excellently balanced in whitening resistance, abrasion resistance and heat sealability, and a composition having excellent rubbery properties, thermal resistance, abrasion resistance and flexibility are provided. A composition comprising a specific propylene•α-olefin copolymer for which, in a signal chart measured by 13C-NMR and predetermined such that the peak present at the highest magnetic field among the signals originating from CH (methine) of the constituent unit derived from an α-olefin having 4 to 20 carbon atoms is to be at 34.4 ppm, an absorption intensity A at about 22.0 to 20.9 ppm and an absorption intensity B at about 19.0 to 20.6 ppm satisfy the following relational expressions (i) and (ii) with respect to an absorption intensity C at about 19.0 to 22.0 ppm, which is assignable to propylene methyl: (A/C)×100≦8  (i), and (B/C)×100≧60  (ii), a molded product thereof, and the α-olefin-based copolymer are provided.