An olefin metathesis process for converting a reactant olefin or a mixture of reactant olefins into one or more product olefins that are different from the reactant olefin(s). The process employs a catalyst system containing a carbene-generating agent and a bimetallic ruthenium complex comprising one or more μ-hydrido bridging ligands, and optionally containing di(t-butyl)phosphine. The catalyst system is advantageously active at process temperatures greater than 90° C. Cyclization metathesis and ring-opening polymerization metathesis are preferred olefin metathesis processes.