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 one or more rings, in the presence of a catalyst formed from a metallocene as transition-metal compound and a cocatalyst, wherein the metallocene is a compound of the formula I ##STR12## in which M.sup.1 is a metal from group IVb, Vb or VIb of the Periodic Table,
- 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, an OH group or a halogen atom,
- the radicals R.sup.3 are identical or different and are a hydrogen atom, a halogen atom, a C.sub.1 -C.sub.10 -alkyl group, which may be halogenated, a C.sub.6 -C.sub.10 -aryl group,
- an --NR.sup.16.sub.2, --SR.sup.16, --OSiR.sup.16.sub.3, --SiR.sup.16.sub.3 or --PR.sup.16.sub.2 radical, in which R.sup.16 is a halogen atom, a C.sub.1 -C.sub.10 -alkyl group or a C.sub.6 -C.sub.10 -aryl group,
- the radicals R.sup.8 are identical or different and are a C.sub.1 -C.sub.10 -alkyl group, a C.sub.6 -C.sub.10 -aryl group, an --NR.sup.16.sub.2, --SR.sup.16, --OSiR.sup.16.sub.3, --SiR.sup.16.sub.3 or --PR.sup.16.sub.2 radical, in which R.sup.16 is a halogen atom, a C.sub.1 -C.sub.10 -alkyl group or a C.sub.6 -C.sub.10 -aryl group,
- R.sup.4 to R.sup.7 and R.sup.8 to R.sup.12 are identical or different and are hydrogen atom, a halogen atom, a C.sub.1 -C.sub.10 -alkyl group, which may be halogenated, a C.sub.6 -C.sub.10 -aryl group, an --NR.sup.16.sub.2, --SR.sup.16, --OSiR.sup.16.sub.3, --SiR.sup.16.sub.3 or --PR.sup.16.sub.2 radical, in which R.sup.16 is a halogen a C.sub.1 -C.sub.10 -alkyl group or a C.sub.6 -C.sub.10 -aryl group, or adjacent radicals R.sup.4 to R.sup.12, together with the atoms connecting them, form one or more aromatic or aliphatic rings, or the radicals R.sup.5 and R.sup.8 or R.sup.12,together with the atoms connecting them, form an aromatic or aliphatic ring, R.sup.13 is ##STR13## .dbd.BR.sup.14, .dbd.AlR.sup.14, --Ge--, --O--, --S--, .dbd.SO, .dbd.SO.sub.2, .dbd.NR.sup.14, .dbd.CO, .dbd.PR.sup.14 or .dbd.P(O) R.sup.14,
- where R.sup.14 and R.sup.15 are identical or different and are a hydrogen atom, a halogen atom, a C.sub.1 -C.sub.10 -alkyl group, a C.sub.1 -C.sub.10 -fluoroalkyl 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 -fluoroaryl 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 or a C.sub.8 -C.sub.40 -arylalkenyl group, or R.sup.14 and R.sup.15, in each case together with atoms connecting them, form one or more rings, and
- M.sup.2 is silicon, germanium or tin.