Abstract: The production of polymers containing terminal halogen groups from cationically polymerizable monomers using a metal halide boiling below 50.degree. C. at normal pressure as catalyst and an organic halide corresponding to the following general formula ##STR1## in which X is halogen,n is an integer of 1, 2, 3 or 4,R.sub.1 and R.sub.2 represent C.sub.5 -C.sub.10 cycloalkyl or linear or branched C.sub.1 -C.sub.20 alkyl andR.sub.3 represents C.sub.5 -C.sub.10 cycloalkyl, linear or branched C.sub.1 -C.sub.20 alkyl, C.sub.5 -C.sub.10 cycloalkylene, linear or branched C.sub.1 -C.sub.20 alkylene or aryl, and the organic halide (inifer) contains from 5 to 50 carbon atoms and is present in concentrations of from 10.sup.-1 to 10.sup.-6 moles per mole monomer while the metal halide is added in a 1.1 to 100-fold molar excess, based on halogen atoms of the organic halide, at temperatures of from +10.degree. to -130.degree. C.