Polymerization of isobutylene

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, based on isobutylene employed, of boron trifluoride catalyst, in the presence or absence of from 10 to 5,000 ppm, based on the weight of isobutylene employed, of molecular weight regulators and/or in the presence of from 10 to 5,000 ppm, based on the weight of isobutylene employed, of a primary or secondary alcohol as polymerization accelerator, and in the presence of from 30 to 90 percent by weight, based on isobutylene employed, of a low-boiling solvent which is inert under the reaction conditions, the solvent vaporized during the polymerization being drawn off continuously, liquefied and recycled, in the liquid state, to the polymerization zone, wherein a boron trifluoride catalyst which contains less than 0.3 percent by volume of silicon tetrafluoride is used and the solvent is recycled not less than twice during the continuous polymerization.