There are herein disclosed an olefin copolymer which comprises an olefin unit and a diolefin unit and in which a weight-average molecular weight is in the range of 200 to 800,000, the content of the diolefin unit is in the range of 0.002 to 30 mol%, and a ratio TUS/DOU between the total content of unsaturated groups observed in a molecular chain (TUS mol%) and the content of the diolefin unit (DOU mol%) is in the range of 0.001 to 200; an olefin graft copolymer obtained by the graft polymerization of this olefin copolymer and an olefin; a hydrogenated olefin copolymer and olefin graft copolymer thereof; and a process for preparing these copolymers.These olefin copolymers are excellent in molding/working properties and have a good thermal stability, transparency and uniformity. Therefore, they are useful as a high-performance VLDPE, LDPE, L-LDPE and HDPE, and further useful as a novel branched propylene polymer, a thermoplastic elastomer, a compatibilizing agent for other resins, and the like.