Abstract: Polymers of C.sub.2 -C.sub.10 -alk-1-enes are prepared at from 0.5 to 3000 bar and from -50.degree. to 300.degree. C. using a catalyst system by a process in which the catalyst system used is one which contains, as active components:a) a metallocene complex of the general formula I ##STR1## where M is titanium, zirconium, hafnium, vanadium, niobium or tantalum,X is fluorine, chlorine, bromine, iodine, hydrogen, C.sub.1 -C.sub.10 -alkyl, C.sub.6 -C.sub.15 -aryl or --OR.sup.7,R.sup.7 is C.sub.1 -C.sub.10 -alkyl, C.sub.6 -C.sub.15 -aryl, alkylaryl, arylalkyl, fluoroalkyl or fluoraryl, where each alkyl radical is of 1 to 10 carbon atoms and each aryl radical is of 6 to 20 carbon atoms,R.sup.1 to R.sup.6 are each hydrogen, C.sub.1 -C.sub.10 -alkyl, 5-membered to 7-membered cycloalkyl, which in turn may carry C.sub.1 -C.sub.10 -alkyl radicals as substituents, C.sub.6 -C.sub.15 -aryl or arylalkyl, where two adjacent radicals together may furthermore be a cyclic group of 4 to 15, carbon atoms, or Si(R.sup.8).sub.3R.