The present invention relates to a process for the production of highly reactive polyisobutenes with a content of terminal vinylidene groupings of greater than 80 mol % and an average molecular weight of 500 to 10,000 Dalton by cationic polymerization of isobutene or of isobutene and monomers copolymerizable with isobutene in the presence of solvent-stabilized transition metal complexes with weakly coordinated anions.