The kinetics of homogeneous deep oxidation of methane in lean mixtures (up to 2 vol % CH4 in air) in ceramic tubes and fixed beds of ceramic spheres was studied. Experiments with the homogeneous reaction have shown that the methane oxidation occurs via a consecutive scheme through CO formation. The reaction rate of CH4 oxidation was found to depend upon the equivalent pass diameter with a significant reaction inhibition in packing of small tubes and spheres, reflecting the influence of mass transfer on the radical-chain termination at the ceramic surfaces. It was also found that CO oxidation practically does not depend upon the mass exchange conditions, but it is visibly inhibited by methane. Recommended kinetic equations and their parameters are presented.