Two reaction pathways for hydrocarbon chain-growth mechanisms over Ru(0001) in Fischer-Tropsch synthesis have been analyzed using periodic ab initio calculations for 25% coverage. Adsorption energies for the intermediates for the first two catalytic cycles for each mechanism as well as the transition states are reported. Both mechanisms are carbene-type mechanisms. Adsorbed CH species are used as the building unit, rather than adsorbed CH2 intermediates. The resulting intermediate hydrocarbon chains at the surface are alkyl- and alkylidenelike, respectively.