Abstract: The synthesis of methane from CO and CO₂ by hydrogenation is now considered as a promising route in effectively storing hydrogen energy as well as sustainably producing fuels and chemicals, while many reaction details involved in such processes, in particular for the hydrogenation of the CO and CO₂ mixture, are not yet adequately understood. As a supplement to our previous works on the hydrogenation of CO and CO₂ into alcohols and hydrocarbons, a thermodynamic consideration is made in this work to evaluate the potential and limit for the synthesis of methane from CO, CO₂, and their mixture in particular. The results consolidate that in comparison with single CO or CO₂, their mixture is probably more credible in practice for the production of methane by hydrogenation, where the overall C-based methane yield can be used as the major index to evaluate the process efficiency. The hydrogenation of CO shows a higher equilibrium yield of methane than the hydrogenation of CO₂, while the overall C-based equilibrium yield of methane for the hydrogenation of the CO and CO₂ mixture just lies in between and decreases almost lineally with the increase of the CO₂/(CO+CO₂) molar ratio in the feed, despite the great change in the equilibrium conversions of CO and CO₂ with the feed composition. Nevertheless, an adequate overall C-based equilibrium yield of methane (> 85%) can be achieved at a temperature lower than 400 ℃ and a pressure higher than 0.1 MPa for the stoichiometric hydrogenation of CO, CO₂, or their mixture whichever. These results should be beneficial to the design of more efficient catalysts and processes for the hydrogenation of CO and CO₂ to methane.