Preparation of isobutene homopolymers or copolymers having a number average molecular weight of from 500 to 5 000 000 by polymerization of isobutene or an isobutene-comprising monomer mixture in the presence of a Lewis acid or a complex comprising a Lewis acid as polymerization catalyst, wherein the polymerization is carried out in the presence of at least one hemiacetal or full acetal which can be obtained by protic acid-catalyzed reaction of at least one C1-C12-hydrocarbyl alcohol with at least one aldehyde or ketone having from 1 to 12 carbon atoms.