Isobutylene polymers are prepared by polymerizing the monomers at from 0.2 to 20 bar and from -130.degree. and +60.degree. C. in the presence of from 0.01 to 20 mmol of a boron halide catalyst system which contains as cocatalyst a carboxylic anhydride or carbonyl halide, preferably an aliphatic or aromatic, unsubstituted or halogen-substituted C.sub.4 -C.sub.18 -carboxylic anhydride of C.sub.2 -C.sub.12 -carbonyl halide and where appropriate also a customary polymerization accelerant in customary amounts, in the presence or absence of an inert solvent with dissipation of the heat of reaction.