A method for selectively hydrogenating a polymer containing monomer units from at least two different conjugated diolefins, one of which conjugated diolefins is more substituted at the 2, 3 and/or 4 carbon atoms than is the other. The selective hydrogenation can be accomplished with selective hydrogenation catalysts known in the prior art at selected conditions such that ethylenic unsaturation incorporated into the polymer from the lesser substituted conjugated diolefin is hydrogenated while at least a portion of the ethylenic unsaturation incorporated into the polymer by the more substituted conjugated diolefin remains unsaturated. The polymer containing monomer units from at least two different conjugated diolefins may also contain one or more other monomers, particularly monoalkenyl aromatic hydrocarbon monomers. The hydrogenated polymer may be random, tapered or block. The hydrogenated polymers, which will contain a controlled amount of residual ehtylenic unsaturation in the conjugated diolefin portion, may be used in any application in which a completely hydrogenated polymer would be useful. Moreover, the selectively hydrogenated polymer of this invention may be used in compositions where polymers capable of cross-linking through ethylenic unsaturation are required. The selectively hydrogenated polymer of this invention may also be functionalized using methods requiring reaction with ethylenic unsaturation.