Abstract: Metallocenes containing aryl-substituted indenyl derivatives as ligands, process for their preparation, and their use as catalysts.A very effective catalyst system for the polymerization or copolymerization of olefins comprises a cocatalyst, preferably an aluminoxane or a supported aluminoxane, and a metallocene of the formula I ##STR1## in which, in the preferred form, M.sup.1 is Zr or Hf, R.sup.1 and R.sup.2 are halogen or alkyl, R.sup.1 is alkyl, R.sup.4 to R.sup.12 are alkyl or hydrogen and R.sup.13 is a (substituted) alkylene or heteroatom bridge.The metallocenes, in particular the zirconocenes, produce polymers of very high molecular weight, in the case of prochiral monomers polymers of very high molecular weight, very high stereotacticity and very high melting point, at high catalyst activities in the industrially particularly interesting temperature range between 50 and 80.degree. C. In addition, reactor deposits are avoided by means of supported catalyst systems.