Abstract: A process for the preparation of a polyolefin wax by polymerization or copolymerization of olefins or diolefins in suspension and in the presence of a catalyst. The process utilizes a metallocene and a cocatalyst, wherein the metallocene is a compound of the formula I ##STR1## in which M.sup.1 is a metal of group IVb, Vb or VIb of the Periodic Table of Elements, R.sup.1 and R.sup.2 are identical or different and are a hydrogen atom, a C.sub.1 -C.sub.10 -alkyl group, a C.sub.1 -C.sub.10 -alkoxy group, a C.sub.6 -C.sub.10 -aryl group, a C.sub.6 -C.sub.10 -aryloxy group, a C.sub.2 -C.sub.10 -alkenyl group, a C.sub.7 -C.sub.40 -arylalkyl group, a C.sub.7 -C.sub.40 -alkylaryl group, a C.sub.8 -C.sub.40 -arylalkenyl group or a halogen atom and R.sup.3 and R.sup.4 are identical or different and are a mononuclear or polynuclear hydrocarbon radical which may form a sandwich structure with the central atom M.sup.