A kinetic model was developed for the heterogeneously catalysed oxidative coupling of methane for temperatures between 923 and 1023 K, inlet methane-to-oxygen ratios of 2 to 12, and oxygen conversions between 10 and 100%. This model features 10 catalytic reactions coupled to 39 gas-phase chain reactions and accounts for irreducible mass-transport limitations for reactive intermediates. The observed conversions and selectivities are adequately described up to 200 kPa total pressure. The observed strong increase of the conversions between 200 and 1000 kPa is described qualitatively. The catalyst not only produces radicals but also acts as an important radical quencher. Regeneration of the active sites through water desorption was found to be a kinetically significant step in the catalytic sequence producing methyl radicals. At atmospheric pressure approximately 90% of the methane and oxygen is converted on the surface of Sn/Li/MgO, the balance being converted through branched-chain reactions in the pores of the catalyst and in the interstitial phase. For Li/MgO only one-third of the methane is converted on the catalyst surface. For Sn/Li/MgO the catalytic oxidation of methyl radicals, rather than gasphase reactions, limits the selectivity toward C-2 products.