Coordination catalyst systems

A process for preparing unsaturated hydrocarbon compounds by a catalyzed metathesis reaction of alkenes or alkynes, comprising subjecting to conditions effective for metathesis alkenes or alkynes in the presence of a metathesis catalyst which is a coordination catalyst system, based on a transition metal compound of subgroup IV to VIII and a cyclic organometallic compound of main group III of the periodic table of elements, wherein said cyclic organometallic compound is a compound of the formulae I or II ##STR3## in which M is B, Al, Ga, In,

• X.sup.1, X.sup.2, X.sup.3 are, in each case independently of one another, CHR.sup.1, NR.sup.2, O, S,
• Y.sup.1, Y.sup.2 are, in each case independently of one another, --(CH.sub.2).sub.m --, o-(CH.sub.2).sub.p --C.sub.6 H.sub.4 --(CH.sub.2).sub.q, o-(CH.sub.2).sub.p --C.sub.6 H.sub.6 --(CH.sub.2).sub.q, o-(CH.sub.2).sub.q --C.sub.6 H.sub.8 --(CH.sub.2).sub.q, o-(CH.sub.2).sub.p --C.sub.6 H.sub.10 --(CH.sub.2).sub.q, o-(CH.sub.2).sub.p --C.sub.5 H.sub.4 --(CH.sub.2).sub.q, o-(CH.sub.2).sub.p --C.sub.5 H.sub.6 --(CH.sub.2).sub.q, o-(CH.sub.2).sub.p --C.sub.5 H.sub.8 --(CH.sub.2).sub.q, --(CH.sub.2).sub.p --CH.dbd.CH.dbd.(CH.sub.2).sub.q
• Z is NR.sup.3 R.sup.4, PR.sup.3 R.sup.4, OR.sup.5, SR.sup.5
• R.sup.1 is H, OH, halogen, C.sub.1-6 -alkyl or C.sub.1-6 -alkoxy, C.sub.5-7 -cycloalkyl, phenyl,
• R.sup.2, R.sup.3, R.sup.4, R.sup.5 are, in each case independently of one another, H or C.sub.1-6 -alkyl, C.sub.5-7 -cycloalkyl, phenyl, R.sup.3 and R.sup.4 together also a C.sub.4-6 -alkylene bridge, m
• m is a number from 1 to 6,
• p, q are, in each case independently of one another, a number from 0 to 2, ##STR4## having M, R.sup.2 and R.sup.3 as defined above and in which Z' is N, P,
• a is a number from 2 to 4,
• b, c are the number 0 or 1 with b+c=1.