The present invention relates to a process for preparing high-reactivity isobutene homo- or copolymers with a content of terminal vinylidene double bonds per homo- or copolymer 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 of an alkylaluminum halide-donor complex, said complex comprising, as the donor, a mixture of at least two organic compounds with at least one ether function each.