The combustion of lean CH4/O-2/N-2 mixtures on a polycrystalline platinum foil in a stagnation point flow reactor at atmospheric pressure and at steady state is studied experimentally and the results reproduced using a numerical code. The dependences of the methane conversion efficiency and of the CO selectivity on the platinum surface temperature were used as the basis for the comparison between experiments and modelling. The simulations employed both a global and a detailed chemical kinetic approach to the heterogeneous and homogeneous oxidation mechanisms. The predicted temperatures of the catalytic and homogeneous ignitions were in good agreement with those of the present experiments as well as those of previous studies. After a minor adjustment of one sensitive parameter of both chemical kinetic mechanisms, the predicted curves of methane conversion as a function of surface temperature closely reproduced their experimental counterparts. The experiments showed that the fuel conversion in the heterogeneous combustion regime was not affected by the degree of nitrogen dilution, the fuel mixture strength, nor the number of thermal cycles undergone by the foil, even though these caused morphological changes of the Pt surface. However, ageing of the catalyst resulted in a reduction of the surface temperature for which the homogeneous combustion reverted back to heterogeneous combustion when decreasing the electrical power to the foil. It also caused higher CO selectivities and fuel conversions in the homogeneous combustion regime. Varying the nitrogen dilution for a same fuel mixture strength augmented both the peak homogeneous fuel conversion and the hysteresis effects, while simultaneously lowering the CO selectivity. Decreasing the fuel mixture strength for a particular nitrogen dilution caused homogeneous ignition to occur at lower surface temperatures and attenuated hysteresis effects. According to the modelling results obtained with the detailed chemical mechanism, the surface reactions inhibited in several ways the extent of the gas-phase oxidation and increased the surface temperature of homogeneous ignition.