Preparation of high-reactivity isobutene homo- or copolymers with a content of terminal vinylidene double bonds per polyisobutene chain end of at least 50 mol% by polymerization of isobutene or isobutene-comprising monomer mixtures in the presence of Lewis acids suitable as polymerization catalysts or of complexes which are effective as polymerization catalysts and are formed from Lewis acids and donors, and in the presence of initiators, wherein the initiators used are organic sulfonic acids Z-SO3H in which the variable Z denotes an alkyl radical, haloalkyl radical, cycloalkyl radical, aryl radical or arylalkyl radical.