A ring-opened metathesis copolymer and its hydrogenated product having a desired monomer unit ratio and a high molecular weight and having hydroxyl groups or hydroxycarbonyl groups can be obtained by conducting a ring-opening metathesis copolymerization of a norbornene-type monomer having hydroxyl groups or hydroxycarbonyl groups with an unsubstituted norbornene-type monomer having at least three rings in the presence of a catalyst predominantly comprised of an organic ruthenium compound having coordinated therewith a neutral electron-donating ligand, and, if desired, hydrogenating the resulting copolymer. The thus-obtained ring-opened metathesis copolymer and its hydrogenation product are characterized by having a low water absorption, good adhesion to metal and other materials, good compatibility with a curing agent and other compounds, and high heat resistance, and exhibiting reduced signal retardation and signal noise.