Two processes have been developed for the selective hydrogenation of the C=C bonds in nitrile-butadiene rubber emulsions (NBR emulsions) in the presence of a number of RuCl2(PPh3)(3) complex catalysts. One of the processes is carried out in a homogeneous system, in which an organic solvent, which can dissolve the NBR polymer and catalyst and which is compatible with the emulsion, is used. The other process is carried out in a heterogeneous system, in which an organic solvent which is capable of dissolving the catalyst and swelling the polymer particle but is not miscible with the aqueous emulsion phase, is used. In both processes, quantitative hydrogenation of the C=C bonds of the NBR emulsion is achieved in the presence of RuCl2(PPh3)(3). It is also found that the addition of certain types of additives can improve the activities of the Ru-based catalysts.