A process for hydrogenating a diene polymer or copolymer, which comprises contacting said polymer or copolymer having a number average molecular weight of 500 to 1,000,000, in the absence of a hydrocarbon lithium compound, with hydrogen in an inert organic solvent in the presence of at least one of a titanocene diaryl compound having the general formula (I):
- ##STR5## wherein R.sub.1 to R.sub.6 are independent hydrogen atoms or alkyl groups of 1 to 4 carbon atoms, and at least one of R.sub.1 to R.sub.3 and at least one of R.sub.4 to R.sub.6 are alkyl groups and at least one of R.sub.1 to R.sub.3 and at least one of R.sub.4 to R.sub.6 are hydrogen atoms, to selectively hydrogenate 50% or more of the unsaturated double bonds of said polymer or copolymer.