The asymptotic structure of laminar, non-premixed methane flames is analysed using a reduced four-step chemical-kinetic mechanism. Chemical reactions are presumed to take place in two layers: the inner layer and the oxidation layer. In the inner layer the fuel reacts with radicals and the main compounds formed are the intermediate species CO and H2. These intermediate species are oxidized in the oxidation layer. The structure of the oxidation layer is described by two second-order differential equations: one for CO and the other for H2. Two limiting cases are considered. At one limit the global step CO+H2⇌CO2+H2is presumed to maintain partial equilibrium everywhere in the oxidation layer except in a thin layer adjacent to the inner layer. At the other limit the steady-state approximation is introduced for H2everywhere in the oxidation layer except in a thin layer adjacent to the inner layer. This limit, called ‘slow CO oxidation’, has not been analysed previously. The structure of the inner layer is described by two second-order differential equations: one for the fuel and the other for the H radicals. This is a significant improvement over previous models in which either a steady-state approximation is introduced for the H radicals in the inner layer, or the reaction between the fuel and radicals is presumed to be very fast. The chain-breaking elementary reaction CH3+H+M→CH4+M is found to have a significant influence on the structure of the inner layer and on the scalar dissipation rates at extinction. The influence of this reaction was either neglected in previous models or was included as a perturbation to the principal elementary reactions taking place to the leading order in the inner layer. Using the results of the asymptotic analysis the scalar dissipation rates at extinction are calculated at a pressure of 1 bar. They are found to agree well with those calculated numerically using a chemical-kinetic mechanism made up of elementary reactions.