Polymer electrolyte membrane fuel cells (PEMFCs) for household applications utilize H2 produced from natural gas via steam reforming followed by a water gas shift (WGS) unit. The H2-rich gas contains CO2 and small amounts of CO, which is a poison for PEMFCs. Today, CO is mostly converted by addition of O2 and preferential oxidation, but H2 is then also partly oxidized. An alternative is selective CO methanation, studied in this work. CO2 methanation is then a highly unwanted reaction, consuming additional H2. The kinetics of CO methanation in CO2/H2 rich gases were studied with a home-made Ru catalyst in a fixed bed reactor at 1 bar and 160–240 °C. Both CO and CO2 methanation can be well described by a Langmuir Hinshelwood approach. The rate of CO2 methanation is slow compared to CO. CO2 is directly converted to methane, i.e., the indirect route via reverse water gas shift (WGS) and subsequent CO methanation could be excluded by the experimental data and in combination with kinetic considerations. Pore diffusion may affect the CO conversion (>200 °C). The kinetic equations were applied to model an adiabatic fixed bed methanation reactor of a fuel cell appliance.