Synthetic natural gas (SNG) can be obtained via methanation of synthesis gas (syngas). Many thermodynamic reaction details involved in this process are not yet fully understood. In this paper, a comprehensive thermodynamic analysis of reactions occurring in the methanation of carbon oxides (CO and CO₂) is conducted using the Gibbs free energy minimization method. The equilibrium constants of eight reactions involved in the methanation reactions were calculated at different temperatures. The effects of temperature, pressure, ratio of H₂/CO (and H₂/CO₂), and the addition of other compounds (H₂O, O₂, CH₄, and C₂H₄) in the feed gas (syngas) on the conversion of CO and CO₂, CH₄ selectivity and yield, as well as carbon deposition, were carefully investigated. In addition, experimental data obtained on commercial Ni-based catalysts for CO methanation and three cases adopted from the literature were compared with the thermodynamic calculations. It is found that low temperature, high pressure, and a large H₂/CO (and H₂/CO₂) ratio are favourable for the methanation reactions. Adding steam into the feed gas could alleviate the carbon deposition to a large extent. Trace amounts of O₂ in syngas is unfavourable for SNG generation although it can lower carbon deposition. Additional CH₄ in the feed gas almost has no influence on the CO conversion and CH₄ yield, but it leads to the increase of carbon formed. Introduction of a small amount of C₂H₄, a representative of hydrocarbons in syngas, results in low CH₄ yield and serious carbon deposition although it does not affect CO conversion. CO is relatively easy to hydrogenated compared to CO₂ at the same reaction conditions. The comparison of thermodynamic calculations with experimental results demonstrated that the Gibbs free energy minimization method is significantly effective for understanding the reactions occurring in methanation and helpful for the development of catalysts and processes for the production of SNG.