The activity and selectivity of a 2 wt% Ru supported on γ-Al2O3 egg-shell catalyst for CO methanation in CO2/H2 rich gases was investigated. A kinetic model based on a Langmuir-Hinshelwood approach for both reactions was determined. The agreement with measurements in a fixed bed reactor is very satisfactory. CO2 methanation is slow compared to CO methanation, at least at temperatures below 200 ◦C. CO2 is directly converted to methane; the indirect route via RWGS and CO methanation could be excluded by respective measurements and kinetic considerations. Pore diffusion may affect the CO conversionat high temperatures (>200 ◦C). The kinetic equations were applied to model an adiabatic fixed bed methanation reactor suitable for a fuel cell for household appliances. The catalyst mass needed to reach a residual CO content of 100 ppm for feed gas with 0.5% CO, 10% CO2, 10% H2O, and 79.5% H2 is about 3 kg, which seems to a reasonable value. The H2 consumption is 20% higher compared to the ideal case without any conversion of CO2.