Methane steam reforming is the key reaction to produce synthesis gas and hydrogen at the industrial scale. Here the kinetics of methane steam reforming over a rhodium-based catalyst is investigated in the temperature range 500-800 A degrees C and as a function of CH4, H2O and H-2 partial pressures. The methane steam reforming reaction cannot be modeled without taking CO and H coverages into account. This is especially important at low temperatures and higher partial pressures of CO and H-2. For methane CO2 reforming experiments, it is also necessary to consider the repulsive interaction of CO that lowers the adsorption energy at high CO coverage. The CO-CO interaction is supported by comparison with fundamental surface science studies.