The combustion of methane with an excess of oxygen was examined under transient conditions in a catalytic monolith reactor, The reaction exhibited a sharp light off in the inlet region of the reactor, and essentially complete combustion was attained. The experimental reactor was modeled using a comprehensive two-dimensional finite element simulator previously developed. Theoretical and observed temperatures were well matched in the reactor following complete combustion. The simulator predicted a response of the order of 1-2 s faster than that observed near the inlet to the reactor where the reaction was occurring. Similar agreement was found for startup and shutdown of the reactor, as well as for a situation where the supply of methane to the reactor was interrupted for a period of 16 s. Analysis of the temperature profiles during startup operation showed that the reactor exhibited light off near the entrance, with the heat wave being propagated toward the reactor exit. The Nusselt number exhibited a steady state value of the order of 4, with different values obtained during transient operation. The reaction does not become completely mass transfer controlled in spite of the rapid rise of temperature in the ignition region.