A process for working up a liquid reaction discharge of the cationic polymerization of isobutene, which substantially comprises polyisobutene, unconverted isobutene and an inert diluent, in which the reaction discharge is heated and is let down into a flash container, is described, the reaction discharge separating, as a result of the flashing, into a polyisobutene-containing liquid phase and a gas phase containing the main amount of the isobutene contained in the reaction discharge and of the diluent.