An ethylene-propylene block copolymer comprising a crystalline polypropylene moiety comprising a propylene homopolymer or a copolymer of propylene and not more than one mole% of ethylene or an .alpha.-olefin having 4 or more carbon atoms; and an ethylene-propylene random copolymer moiety having a composition consisting of ethylene and propylene in a weight ratio of ethylene to propylene of 20/80 to 60/40, wherein: (1) said crystalline polypropylene moiety has an intrinsic viscosity ¢n!p of 0.8 to 2.0 dl/g, a specific Q value as a ratio of weight average molecular weight Mw to number average molecular weight Mn of 3.0 to 5.0 as measured by the gel permeation chromatography, and a xylene soluble matter content at 20.degree.C of not more than 1.5% by weight; (2) said ethylene-propylene random copolymer moiety has an intrinsic viscosity ¢?!EP of 3.5 to 8.5 dl/g; and (3) said ethylene-propylene random copolymer moiety accounts for 5 to 20% by weight of the amount of the entire polymer.
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