The present invention relates to a process for preparing high-reactivity isobutene homo- or copolymers with a content of terminal vinylidene double bonds per polyisobutene chain end of at least 70 mol %, which comprises polymerizing isobutene or an isobutene-comprising monomer mixture in the presence of an aluminum trihalide-donor complex effective as a polymerization catalyst or an alkylaluminum halide-donor complex effective as a polymerization catalyst, wherein the aluminum trihalide or alkylaluminum halide is treated with at least one inorganic hydrate.