A process for working up a liquid reaction discharge of the cationic polymerization of isobutene, which substantially comprises polyisobutene, unconverted isobutene and, if required, an inert diluent, is described. Problems with foam formation when the unconverted isobutene is being distilled off are avoided if the heated reaction discharge is let down into a flash container and/or not more than 900 m.sup.3/h of vapor are expelled per square meter of liquid surface and/or the resulting foam is destroyed, for example in a wet cyclone.