The present invention relates to a transition metal compound of the formula I ##STR1## where M.sup.1 is a metal of group IIIb, IVb or Vb of the Periodic Table of the Elements, R.sup.1, R.sup.2, R.sup.3 and R.sup.4 are identical or different and are each a hydrogen atom, a halogen atom, a C.sub.1 -C.sub.40 -hydrocarbon-containing group, an --SiR.sup.5.sub.3, --NR.sup.5.sub.2, --Si(OR.sup.5).sub.3, --Si(SR.sup.5).sub.3 or --PR.sup.5.sub.2 radical, where R.sup.5 are identical or different and are each a halogen atom, a C.sub.1 -C.sub.10 -alkyl group or a C.sub.6 -C.sub.10 -aryl group, or two or more radicals R.sup.1, R.sup.2, R.sup.3 or R.sup.4 together with the atoms connecting them form a ring system, Y are identical or different and are each a hydrogen atom, a C.sub.1 -C.sub.40 -hydrocarbon-containing group, an OH group, a halogen atom or an NR.sup.5.sub.2 group, k is an integer which corresponds to the valence of the transition metal atom M.sup.1 minus two and if Y is a butadiene unit, k is 1, A is a bridge, R.sup.8 is a hydrogen atom, a halogen atom, a C.sub.1 -C.sub.40 -group, an --SiR.sup.5.sub.3, --NR.sup.5.sub.2, --Si(OR.sup.5).sub.3, --Si(SR.sup.5).sub.3 or --PR.sup.5.sub.2 radical, and X is an element of group Va or Vla of the Periodic Table of the Elements. The transition metal compound is suitable as a catalyst component for olefin polymerization.