The invention relates to a complex compound of ruthenium of the general structural formula I in which X1 and X2 may be identical or different and represent an anionic ligand, in which R1 and R2 are identical or different, but may also have a ring, in which R1 and R2 represent hydrogen or/and a hydrocarbon group, in which the ligand L1 is a N-heterocyclic carbene and in which the ligand L2 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 R1, R2, R3 and R4 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′1, R′2, R′3 and R′4 hydrogen or/and hydrocarbon groups.