The asymptotic structure of laminar, moderately rich, premixed methane flames is analyzed using a reduced chemical-kinetic mechanism comprising four global reactions. This reduced mechanism is different from those employed in previous asymptotic analyses of stoichiometric and lean flames, because a steady-state approximation is not introduced for CH3. The aim of the present analysis is to develop an asymptotic model for rich flames, which can predict the rapid decrease of the burning velocity with increasing equivalence ratio phi. In the analysis, the flame structure is presumed to consist of three zones: a preheat zone with a normalized thickness of the order of unity, a thin reaction zone, and a postflame zone. The preheat zone is presumed to be chemically inert, and in the postflame zone the products are in chemical equilibrium and the temperature is equal to the adiabatic flame temperature T-b. In the reaction zone the chemical reactions are presumed to take place in two layers: the inner layer and the oxidation layer. The rate constants of these reactions are evaluated at T-o, which is the characteristic temperature at the inner layer. In the inner layer the dominant reactions taking place are those between the fuel and radicals, and between CH3 and the radicals. An important difference between the structure of the inner layer of rich flames and that of lean flames analyzed previously is the enhanced influence of the chain-breaking reaction CH3 + H + (M) --> CH4 + (M) in rich flames. Here M represents any third body. This reaction decreases the concentration of H radicals, which in turn decreases the values of the burning velocity. In the oxidation layer of rich flames, the reactive-diffusive balance of O-2 is considered. This differs from the structure of the oxidation layer of lean flames where the reactive-diffusive balance of H-2 and CO was of primary interest. The burning velocities calculated using the results of the asymptotic analysis agree reasonably well with the burning velocities calculated numerically using chemical-kinetic mechanisms made up of elementary reactions. The values of the characteristic temperature at the inner layer T-o are found to increase with increasing values of the equivalence ratio and to approach T-b at phi = 1.36. When T-o is very close to T-b, the asymptotic analysis developed here is no longer valid and an alternative asymptotic analysis must be developed for even larger equivalence ratios.