A copolymer of propylene and butene-1, the constituent monomer units of which comprise 20-63 wt. % of propylene and 37-80 wt. % of butene-1, and which exhibits 0.5 or more in the ratio of the sum of the intensities of absorptions observed at about 20.0-21.0 ppm to the sum of the intensities of total absorptions attributable to the methyl groups in the propylene units observed at about 19.0-22.0 ppm in the .sup.13 C-NMR spectrum measured in a 1,2,4-trichlorobenzene solution and 0.05 or more in the intrinsic viscosity measured at 135.degree. C. in a tetralin solution.