Abstract: A process for the preparation of polyisobutylene by polymerizing isobutylene in a polymerization zone which is at from 0.degree. to -130.degree. C., by means of from 0.01 to 1.0 percent by weight of boron trifluoride catalyst, in the presence of a primary or secondary alcohol as polymerization accelerator and in the presence of from 30 to 90% by weight of a low-boiling solvent which is inert under the reaction conditions, wherein the solvent vaporized during the polymerization is continuously drawn off, liquefied and recycled, in the liquid state, to the polymerization zone, and wherein the boron trifluoride catalyst used contains less than 0.3, in particular less than 0.01, percent by volume of silicon tetrafluoride and the solvent, which is preferably ethylene, is recycled not less than twice but not more than 36 times during the continuous polymerization.