Isobutylene polymers are prepared continuously, in aliphatic C.sub.3 -C.sub.6 -hydrocarbons in the presence of soluble cationic polymerization initiators and coinitiators at from -40.degree. to 40.degree. C. and under from 0.01 to 10 bar, and the solvents and monomers vaporized during the polymerization are recycled, by a process in which the liquid stream of the monomer solution, containing 40-95, in particular 50-85, percent by weight of the monomers, the liquid streams of the recycle and of the coinitiator solution and the separate stream of the initiator solution are combined in a first zone containing the polymerization zone, and the resulting polymer solution is taken off continuously through a second zone vertically below the first zone. The liquid streams of the monomer solution, the coinitiator solution and the recycle can furthermore be fed into the first zone separately from one another.