A propylenic polymer according to the present invention or a composition thereof have an excellent melt flowability and contains a less amount of stickiness-causing components, and also has a low modulus and is pliable, and is capable of providing a transparent molded article, thus being useful as a substitute for a pliable vinyl chloride resin. In addition, a molded article made therefrom exhibits an excellent heat seal performance at a low temperature, and is excellent in terms of transparency and rigidity. Specifically, it has an isotactic pentad fraction (mmmm), which indicates a stereoregulariry, of 30 to 80%, a molecular weight distribution (Mw/Mn) of 3.5 or less and an intrinsic viscosity [.eta.] of 0.8 to 5 dl/g.