The reaction pathways of two types of the carbon-carbon bond-forming reactions catalyzed by thiolate-bridged diruthenium complexes have been investigated by density-functional-theory calculations. It is clarified that both carbon-carbon bond-forming reactions proceed through a ruthenium-allenylidene complex as a common reactive intermediate. The attack of pi electrons on propene or the vinyl alcohol on the ruthenium-allenylidene complex is the first step of the reaction pathways. The reaction pathways are different after the attack of nucleophiles on the ruthenium-alkynyl complex. In the reaction with propene, the carbon-carbon bond-forming reaction proceeds through a stepwise process, whereas in the reaction with vinyl alcohol, it proceeds through a concerted process. The interactions between the ruthenium-allenylidene complex and propene or vinyl alcohol have been investigated by applying a simple way of looking at orbital interactions.