CO and CO2 methanation at steady states and under transient states was conducted over Ni, Ni/Al2O3, Ni/SiO2 and Ru/SiO2. The CO2 methanation proceeded highly selectively as compared with the CO methanation. In the CO methanation, weakly adsorbed CO retarded the hydrogenation of surface carbon species. In the CO2 methanation, the retardation was absent. The selectivity for the CO2 methanation was estimated from the selectivity for the CO methanation, the extent of the retardation and the ratio of the steady state rates of these reactions. The selectivity estimated was in fair agreement with that experimentally obtained.