Polymerization slurries of elastomeric isoolefin homopolymers and copolymers, such as butyl rubber, in diluents such as methyl chloride are effectively stabilized against agglomeration of polymer particles through addition of minor proportions of an hydrogenated preformed copolymer stabilizer having both a lyophobic and a lyophilic portion. The chemical and structural nature of the lyophobic and lyophilic portions which comprise the copolymer stabilizer are significant in determining the extent and method of hydrogenation for production of the most effective stabilizer. Agglomeration of polymer products is effectively prevented, yielding a number of significant processing advantages. The process is especially adaptable to the production of isobutylene-isoprene butyl rubber.