Premixtures of graphite-methane-air have been burned in a flat laminar flame at a pressure of 0.16 atm. A fluidized bed was employed to entrain graphite particles of 4 mum diameter. The extended reaction zone enabled reliable measurements to be obtained of species concentrations, gas velocities, and temperatures. The measurements to a large degree validated the predictions of a one-dimensional mathematical model of the combustion. The model couples detailed carbon particle and gas-phase chemical kinetics, as well as radiative energy exchanges. Some limitations arise because the experimental flame is not truly one dimensional and also because of uncertainties in the chemical kinetics of the richer mixtures. Allowance for radiation improves the accuracy of the predictions, although its influence is not great. Earlier predictions that active radicals in the gas-phase catalyze the char oxidation are supported. The general validity of the model is the springboard for a related model for ultrafine coal combustion. This retains the coupled kinetics and radiation, but adds a coal devolatilization rate to the kinetic scheme and assumes the volatiles to consist entirely of methane, which mixes rapidly with the surrounding gas. Despite these restrictive assumptions, the model reveals important aspects of coal flame combustion and predicts a laminar burning velocity close to that measured.