There are many experimental demonstrations of oscillatory behaviour during methane oxidation over Ni catalysts however the origin of the nonlinear behaviour in this system is not clearly understood yet. The new kinetic scheme for methane oxidation over Ni catalysts and mathematical model of the nonlinear reaction dynamics are developed. The model is derived in the mean field approximation and describes qualitatively the main properties of oscillatory behaviour observed experimentally during the reaction of methane oxidation over Ni catalysts. It was demonstrated that thermokinetic oscillations in this system originate due to periodic oxidation-reduction of the catalyst surface, the variation of the selectivity of the process and the competition of reactants for the free active sites. (c) 2006 Elsevier B.V. All rights reserved.