A computational study of steady, rod-stabilized, inverted, lean, CH 4-air and H 2-CH 4-air flames is conducted. For the CH 4-air flames, either decreasing the inlet equivalence ratio or increasing the mean inflow velocity leads to a larger standoff distance, and below a critical value of the inlet equivalence ratio or above a critical value of the inflow velocity, the flame blows off. For the H 2-CH 4-air flames, decreasing the inlet equivalence ratio has similar effects as those on the CH 4-air flames; however, increasing the inflow velocity reduces the standoff distance. Though counter-intuitive, the predicted behaviour of the flames is consistent with the experimental observations. Both the CH 4-air and H 2-CH 4-air flames exhibit preferential diffusion effects such as superadiabatic temperatures and local equivalence ratio variations, which are more pronounced for the H 2-CH 4-air flames, displaying non-uniform and localized consumption rates of the fuel components. The strong diffusion of H 2 plays an important role to maintain and even strengthen the reaction processes in the anchoring region and the counter-intuitive stabilization/blow-off of the H 2-CH 4-air flames.