Cu-II compounds coordinated octahedrally with nitriles and associated with bulky, non-coordinating counter ions can be applied in the polymerization of isobutene at 30 degrees C. High yields and a high content of terminal double bonds are reached in the resulting highly reactive polyisobutylenes, while the molecular masses are moderate. Two of the coordinating nitriles are more weakly coordinated than the other four, as can be concluded from an exemplary X-ray structure and from vibrational spectra, thus providing easily accessible sites for substrate coordination.