Catalytic combustion and conversion of methane is investigated numerically for transient one-dimensional flow confrgurations (catalytic foil and catalytic wire). The reactive flow is coupled with the processes at the gas-surface interface. The analyses include detailed reaction mechanisms in the gas phase and on the surface as well as a detailed transport model. Computational tools are applied to study the ignition of heterogeneous methane oxidation on a platinum foil and the transition from heterogeneous to homogeneous combustion in this system. Furthermore, the interaction of gas phase and surface reactions in catalytic conversion of methane is considered. Time-dependent selectivity and conversion are calculated.