Abstract: High molecular weight polymers and highly unsaturated polymers (e.g. butyl rubber) are prepared by homopolymerizing and copolymerizing olefins, isoolefins, conjugated multiolefins, or mixtures of isoolefins and conjugated multiolefins with a catalyst system comprising an organoaluminum compound in conjunction with a cocatalyst selected from the group consisting of sulfur dioxide, sulfur trioxide, halogens, mixed halogens and hypohalides.