The present invention describes the use of cationic vinylidene, allenylidene and higher cumulenylidene complexes of ruthenium or osmium as catalysts or catalyst precursors for olefin metathesis reactions of all types, as well as to new cationic allenylidene complexes of ruthenium and osmium which can be used as metathesis catalysts with preferred embodiment. These catalysts or catalyst precursors are easy to prepare from well accessible, stable and essentially non toxic starting materials, can be isolated and stored, they exhibit a high catalytic activity, a good compatibility with functional groups, solvents, water and additives, and they need not to be activated by any additive. Olefins of all types can be used as the substrates in the present invention in ring closing metathesis (RCM) of acyclic dienes and polyenes, the metathesis of enynes and dienynes, the ring opening metathesis polymerization (ROMP) of cyclic olefins, the acyclic diene metathesis polymerization (ADMET) of acyclic dienes or polyenes, the depolymerization of olefinic polymers, and the cross metathesis of two or more olefins. The present invention also applies to combinations of these types of metathetic reactions and domino processes thereof.