A process for preparing halogen-free, reactive polyisobutene having a terminal double bond content of more than 60 mol % and an average molecular weight Mn of 800-3000 dalton by cationic polymerization in the liquid phase of isobutene over an acidic, essentially halogen-free heterogeneous catalyst, where a) a hydrocarbon mixture of essentially C4-hydrocarbons comprising isobutene in an amount of from 10 to 80% by weight is used as the starting material and b) polymerization is carried out continuously at from −30 to 0° C. with average starting material residence times of one hour or less, where the temperature and the residence time are selected such that the isobutene conversion is less than 60% and, after separation from the resulting polyisobutene, the isobutene is either enriched in the partially converted hydrocarbon mixture and returned to the polymerization or passed to another isobutene reaction coupled with the polymerization.