Butyl rubber is a copolymer of mainly an isomonoolefin with a small quantity of an acyclic conjugated diene monomer. The vulcanized butyl rubber possesses relatively good resistance to degradation by heat, oxygen and ozone, and also exhibits remarkably low permeability to gases. Butyl rubber is, however, for various applications, not hard enough. Therefore, the problem exists to increase the hardness of the butyl rubber. Furthermore, it would be desirable for special applications to increase the hardness of the butyl rubber and to reduce its resilience.