A process for the preparation of an olefin polymer by polymerization or copolymerization of an olefin of the formula R.sup.a--CH.dbd.CH--R.sup.b, in which R.sup.a and R.sup.b are identical or different and are a hydrogen atom or a hydrocarbon radical having 1 to 14 carbon atoms or R.sup.a and R.sup.b, together with the atoms connecting them, can form a ring, at a temperature of from -60.degree. to 200.degree. C., at a pressure of from 0.5 to 100 bar, in solution, in suspension or in the gas phase, in the presence of a catalyst formed from a metallocene in the meso-form or a meso:rac mixture, with meso:rac>1:99, as transition-metal compound and a cocatalyst, wherein the metallocene is a compound of the formula I, ##STR00001## in which M.sup.1 is Zr or Hf, R.sup.1 and R.sup.2 are identical or different and are methyl or chlorine, R.sup.3 and R.sup.6 are identical or different and are methyl, isopropyl, phenyl, ethyl or trifluoromethyl, R.sup.4 and R.sup.5 are hydrogen or as defined for R.sup.3 and R.sup.6, or R.sup.4 forms an aliphatic or aromatic ring with R.sup.6, or adjacent radicals R.sup.4 form a ring of this type, and R.sup.7 is a ##STR00002## radical, and m plus n is zero or 1.