Chemically homogeneous cycloolefin copolymers of polycyclic olefins, for example norbornene or tetracyclododecene, with cycloolefins and/or acyclic olefins are obtained without ring opening and in high space-time yields if a catalyst system is used which comprises an aluminoxane and a stereorigid metallocene compound of an element from groups IVb to VIb, of the formula IMAGE the part of the metallocene molecule formed by M1 and the substituents R16-R17 having C1 symmetry or being in the meso form.
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