The methane/oxygen/steam mixture conversion in a porous medium reactor is investigated numerically. The two-temperature (gas/solid) one-dimensional model is employed. The model of the kinetics includes a set of gas-phase radical-chain reactions supplemented with the loss of radicals on the surface of inert solid, formation of soot and reactions of the latter with oxygen, water, and carbon dioxide. The computational experiment showed that the traveling (superadiabatic) reaction front establishes within the reactor. However, in contrast to predictions of thermodynamic models, owing to short residence time at a high temperature, the steam conversion reaction does not develop under the conditions studied. (C) 2013 Elsevier B.V. All rights reserved.