To provide a propylene-based copolymer and a propylene-based copolymer composition, each of which has a high melt tension because it has a long-chain branched structure, exhibits excellent molding processability during molding, such as inflation molding, extrusion molding, blow molding, injection molding or vacuum forming, and is capable of favorably providing a foamed product having an excellent expansion ratio and excellent cell uniformity in the foaming stage. The propylene-based copolymer (A) of the present invention comprises 50 to 95% by mol of constituent units [i] derived from propylene, 4.9 to 49.9% by mol of constituent units [ii] derived from an α-olefin of 2 to 10 carbon atoms other than propylene and 0.1 to 10% by mol of constituent units [iii] derived from a non-conjugated polyene (with the proviso that the total amount of the constituent units [i], [ii] and [iii] is 100% by mol), and is characterized by satisfying specific requirements (a) and (c).