The paper presents the first mathematical model that can simulate the oscillatory behaviour during methane oxidation over Pd catalysts. The main experimental results are reproduced, including the anti-phase oscillations of the concentrations of the reaction products, CO2 and H2O. In line with the experimental results, it is demonstrated that the oscillations are related to periodic oxidation and reduction of the Pd catalyst. The complicated waveform of the oscillations and the anti-phase oscillations of two reactant products originate due to the periodic accumulation and removal of bulk carbon. The simulation results show that the anti-phase oscillations of CO2 and H2O concentrations can occur only in the case of a high rate of carbon diffusion and a large depth of penetration of carbon into the Pd catalyst. (C) 2012 Elsevier Ltd. All rights reserved.