The effect of the diffusion of oxygen from the volume of the catalyst to its surface on the dynamics of the oxidative coupling of methane was assessed on the basis of a mathematical model of the reaction of methane with the oxidized surface of KNaSrCoO 3-x perovskite. It was shown that the possible values of the diffusion coefficient lie in the range of 10 -18 -10 -16 cm 2 /s characteristic of the diffusion of oxygen in oxide catalysts.Key words: diffusion of oxygen, mathematical modeling, perovskite, oxidative coupling of methane.The diffusion of ions and atoms in the crystal lattice of solids takes place as a result of the movement of point defects. The diffusion process can be realized by various mechanisms depending on the type of defect: exchange of the atoms of the crystalline structure with its vacancies, movement of the atoms along the interstices, simultaneous cyclic replacement of several atoms, etc.[1]. The diffusion effect in a solid catalyst is widely distributed and has a significant effect on the course of the catalytic reactions. This mostly concerns the diffusion of oxygen in metal oxides.Most oxidation processes are realized in the presence of oxygen in the gas phase. Nevertheless there are processes that are preferably realized in a nonstationary regime where the catalyst is alternately oxidized and reduced.The degree of participation of the oxygen of the catalyst is determined by its mobility in the volume of the crystal lattice and the capacity characteristics of the catalyst with respect to oxygen. Thus, in the oxidation of propylene at bismuth molybdate, which has a layer structure, oxygen ions of 500 monolayers in number can take part in the formation of the reaction products [2]. At the same time at catalysts with nonmobile volume oxygen (phosphorus-vanadium, iron-antimony, and others) the oxygen of~2-3rd surface layers enter into the reaction [3,4].The oxide catalysts of oxidation processes include catalysts based on perovskites. In [5] it was shown that in the series of modified perovskite catalysts SrCoO 3 a system with the composition K 0.125 Na 0.125 Sr 0.75 CoO 3-x exhibits the highest activity and selectivity in conjunction with stability of catalytic action in the condensation of methane in the gas phase in the absence of oxygen. In this case the reaction products are formed as a result of reaction of the methane with oxygen on the surface of the catalyst; the decrease of surface oxygen is partly compensated as a result of its diffusion from the volume of the catalyst.It is clear that the effect of the volume oxygen will be minimal if the diffusion is too low. In this connection it seemed of interest to obtain a quantitative estimate of the range of diffusion coefficients of oxygen in the volume of the catalyst in order to 0040-5760/11/4701-0049