The invention relates to a complex compound of ruthenium of the general structural formula I ##STR00001## in which X.sup.1 and X.sup.2 may be identical or different and represent an anionic ligand, in which R.sup.1 and R.sup.2 are identical or different, but may also have a ring, in which R.sup.1 and R.sup.2 represent hydrogen or/and a hydrocarbon group, in which the ligand L.sup.1 is a N-heterocyclic carbene and in which the ligand L.sup.2 is a neutral electron donor, especially a N-heterocyclic carbene or an amine, imine, phosphane, phosphite, stibine, arsine, carbonyl compound, carboxyl compound, nitrile, alcohol, ether, thiol or thioether, wherein R.sup.1, R.sup.2, R.sup.3 and R.sup.4 represent hydrogen or/and hydrocarbon groups. The invention relates also to a process for the preparation of acyclic olefins having two or more carbon atoms or/and of cyclic olefins having four or more carbon atoms from acyclic olefins having two or more carbon atoms or/and from cyclic olefins having four or more carbon atoms by olefin metathesis reaction in the presence of at least one catalyst, wherein such a complex compound is used as catalyst and wherein R'.sup.1, R'.sup.2, R'.sup.3 and R'.sup.4 hydrogen or/and hydrocarbon groups.