There are disclosed a polycyclic norbornene or its derivative ring-opening hydrogenated copolymer which contains 90-10% by mole of a repeating unit represented by the following formula [I] or the alkly-substituted derivative, at least a repeating unit represented by the following formula [II] or the alkly-substituted derivative thereof and, as required, a repeating unit represented by the following formula [III], the alkyl-substituted derivative thereof or the alkylidene-substituted derivative thereof, has an intrinsic viscosity [.eta.] of 0.01-20 dl/g as determined in toluene at 25 .degree. C., and in which at least 50% of the (C C) linkages constituting the main chain are single bonds, and the production of said hydrogenation product ##STR1## wherein represents either a single bond or a double bond.