Abstract: A process of hydrogenation in solution of polymers of conjugated dienes in the presence of homogeneous catalysts which contain, as an essential component, a titanium compound of the type Cp.sub.2 Ti(PhOR).sub.2, where Cp is a cylopentadienyl group, ph a phenyl group, and OR an alkoxide group containing 1 to 4 carbon atoms; or a titanium compound of the type Cp.sub.2 TiR.sub.2, where R is a Ch.sub.2 PPh.sub.2 group.These catalysts are very active in the selective hydrogenation of the double bonds of the diene units of polymers or copolymers of conjugated dienes having number-averaged molecular weights or between approximately 500 and 1,000,000 and, in particular, of random and block copolymers of styrene and butadiene or isoprene, the latter containing at least one styrene block and one polybutadiene and/or polyisoprene block.