Abstract: The invention relates to a process for the preparation of polyolefins by polymerizing olefins of the formula CH.sub.2 CHR in which R=H or C.sub.1 -C.sub.10 alkyl, on their own or as a mixture, if appropriate together with C.sub.4 -C.sub.12 .alpha.,.omega.-diolefins, in solvents, liquid monomers or the gas phase, at temperatures between -50.degree. and 200.degree. C., using a catalyst system composed of a soluble, halogen-containing transition metal compound of the general formula(cyclopentadienyl).sub.2 Me R Halin which R is cyclopentadienyl or a C.sub.1 -C.sub.6 alkyl radical or a halogen, in particular chlorine, Me is a transition metal, in particular zirconium, and Hal is a halogen, in particular chlorine, and a compound, containing aluminum, of the aluminoxane type having the general formulaeAl.sub.2 OR.sub.4 (Al(R)--O).sub.nfor a linear aluminoxane and/or(Al(R)--O).sub.n+2for a cyclic aluminoxane, in which n is a number from 4 to 20 and R is a methyl or ethyl radical, preferably a methyl radical.