The invention relates to a complex of ruthenium of the structural formula I, where X1 and X2 are identical or different and are each an anionic ligand, R1 and R2 are identical or different and can also contain a ring, and R1 and R2 are each hydrogen or/and a hydrocarbon group, the ligand L1 is an N-heterocyclic carbene and the ligand L2 is an uncharged electron donor, in particular an N-heterocyclic carbene or an amine, imine, phosphine, phosphate, stibine, arsine, carbonyl compound, carboxyl compound, nitrile, alcohol, ether, thiol or thioether, where R1, R2, R3 and R4 are hydrogen or/and hydrocarbon groups. The invention further relates to a process for preparing acyclic olefins having two or more carbon atoms or/and 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 an olefin metathesis reaction in the presence of at least one catalyst, wherein a complex is used as catalyst and R′1, R′2, R′3 and R′4 are hydrogen or/and hydrocarbon groups.