Polyisobutenes in which at least 60 mol % of the polymer chains have at least one olefinically unsaturated terminal group are prepared by cationic polymerization of isobutene or isobutene-containing monomer mixtures in the condensed phase by a process in which the polymerization is carried out in the presence of an initiator system comprising i) a Lewis acid selected from covalent metal chlorides and semimetal chlorides and ii) at least one organic compound I having at least one functional group FG which forms a carbocation or a cationic complex with the Lewis acid under the polymerization conditions, where FG is selected from acyloxy, alkoxy and halogen, which are bonded to a secondary or tertiary carbon atom or to an allylic or a benzylic carbon atom, in a solvent inert toward the Lewis acid, the Lewis acid being used in less than the stoichiometric amount, based on the functional groups FG.