Disclosed is a syndiotactic propylene copolymer containing 0.01 to 40 mol % of olefin units containing --OH group in the side chain. Of absorption peaks attributed to the methyl groups of the propylene units on an absorption spectrum by .sup.13 C-NMR of the copolymer, the intensity of an absorption peak observed at about 20.2 ppm is 0.3 or more of the intensity of absorption peaks of all the methyl groups attributed to the propylene units. The copolymer is produced by copolymerizing propylene and an alkenylsilane or alkenylborane compound in the presence of a catalyst system comprising an asymmetric ligands-having transition metal compound and an aluminoxane, followed by heat-treating the resulting propylene-alkenylsilane copolymer in the presence of a trialkylamine oxide and KF.HF or oxidizing and decomposing the resulting propylene-alkenylborane compound copolymer. Also disclosed is a resin composition comprising the copolymer and other polyolefin(s).