Production rates of oxides of nitrogen in laminar methane-air diffusion flames are addressed, with thermal, prompt, and nitrous oxide mechanisms taken into account, as well as consumption processes collectively termed reburn. For this purpose, it is necessary to extend the well-known four-step flame-chemistry description to six steps, with acetylene taken out of steady-state and one-step production of nitric oxide included. Emission indices are calculated as functions of the rate of scalar dissipation at the stoichiometric mixture fraction for near-atmospheric pressures and shown to be in reasonable agreement with results obtained from numerical integrations. The Various mechanisms of NO, production and consumption are verified to be strongly dependent on the flame temperature and on superequilibrium concentrations of radicals, both fuel-derived and from hydrogen-oxygen chemistry; the flame-structure analysis was extended to provide sufficient accuracy in the prediction of these quantities. It was found that for flames in near-normal ambient atmospheres, the prompt mechanism usually is most important. For longer residence times, and especially for ambient pressures and temperatures above standard, the thermal mechanism was found to increase in importance, but this increase was calculated to be offset almost entirely by NO consumption through reburn reactions. Conditions that favor reburn were observed to be those where the ratio of radical concentrations to NO concentrations is small. Longer residence times and higher pressures were demonstrated to lead both to more complete heat release and to smaller superequilibrium radical concentrations whence the correspondence between thermal production and reburn. The nitrous oxide mechanism was found to be generally less important for the conditions considered here.