This paper presents a density functional theory study of the ruthenium-catalyzed clef in metathesis reactions. The ligand binding energy has been calculated in the first generation of Grubbs-type (PCy3)(2)-Cl2Ru=CHPh (pre)catalyst, as well as in the heteroleptic (pre)catalytic systems in which a N-heterocyclic carbene, NHC, ligand substitutes a single phosphine. In agreement with experiments PCy3 coordinates more strongly to Ru in the heteroleptic (pre)catalysts than in the Grubbs-type (pre)catalyst. Moreover, ethene coordination and insertion into the Ru-alkylidene bond in the above-mentioned systems, as well as in the Hofmann type catalytic system with a cis-coordinated phosphane ligand, has been studied. The calculated insertion barrier for the NHC systems are lower than that of the (PCy3)(2)Cl2Ru=CHPh system. This is consistent with the higher activity experimentally observed for the NHC-based system.