Abstract: A propylene-based copolymer composition comprises: 10 to 60% by weight of a polymer component (A) comprising propylene as a main component and having an isotactic index of not less than 90%; and 40 to 90% by weight of a copolymer component (B) comprising propylene and other &agr;-olefin having not more than 8 carbon atoms and containing propylene and ethylene as essential components, the copolymer component containing cold xylene insolubles in an amount of from more than 20 to 70% by weight based on the weight of whole polymers, and cold xylene solubles in an amount of 10 to 60% by weight based on the weight of whole polymers, and cold xylene solubles containing an &agr;-olefin other than propylene in an amount of less than 20% by weight, and the composition being obtained by first producing the component (A) by polymerization and then producing the component (B) by polymerization.