Abstract: A process for preparing a homogeneous random polymer of two or more cationically polymerizable monomers having the general formula: ##EQU1## wherein R.sub.1 is alkyl, alkenyl, phenyl, aralkyl or alkaryl, R.sub.2 is H, alkenyl or alkyl and where R.sub.2 is H, R.sub.1 must be phenyl or alkylaryl, which comprises continuously reacting said monomers in a mixed solvent system comprising a polar organic solvent and a nonpolar, nonaromatic hydrocarbon solvent, said polymerization being carried out in a well-stirred reactor in the presence of a Friedel-Crafts catalyst. The preferred polymer is a homogeneous random styrene-isobutylene copolymer which is prepared by continuously reacting in solution about 10 to about 90 parts by weight of styrene with about 90 to about 10 parts by weight of isobutylene in a mixed solvent system comprising a polar organic solvent and a nonpolar nonaromatic hydrocarbon solvent.