The carbon-carbon coupling of C (carbide) and CH (methylidyne), C and CH2 (methylene), and C and CH3 (methyl) on nickel has been studied with density functional theory using 7- and 13-atom cluster models. Formation of CCH3 (ethylidyne) turned out to be the most exothermic reaction on both clusters, Experimentally, CCH3 has been identified unambiguously with a structure perpendicular to the metal surface. Thus for the C/CH3 coupling forming CCH3, we have determined the structure and potential energy surface in the coadsorbed state, transition state, and CC-formed state. The transition state is explicitly determined on the 7-atom cluster and the 13-atom cluster of both nickel and cobalt. We find transition state barriers of 57 kJ/mol for the Ni-7 cluster, 55 kJ/mol for the Co-7 cluster 84 kJ/mol for the Ni-13 cluster, and 47 kJ/mol for the Co-13 cluster. The overall reaction energies are -215, -184, -66, and -89 kJ/mol, respectively. Analysis of the TS shows a dominant contribution of the CC bond to the reaction coordinate. Cluster size effects play a role in all studied CC coupling reactions.