The catalytic combustion of methane was studied in monolith reactors, at atmospheric pressure and how conditions corresponding to Reynolds numbers in the laminar flow region. The catalyst was palladium based and dispersed on a gamma-alumina washcoat covering a 62 cell cm(-2) ceramic support, with square-shaped cells. Because of the nature of the coating process the thickness of the washcoat varied from approximately 10 mu m on the side to 150 mu m in the corners. Chemical reaction kinetics were determined in a monolith of length 12.7 mm, while performance was measured for a number of lengths up to 151mm. The outside diameter of the monolith was 117mm. Experimental conditions of temperature were between 607-845K with the fuel to air mass ratio fixed at 0.0053. It was shown that at temperatures > 770K, the reaction was limited by transport processes. For a 51mm long monolith, when 76% conversion was achieved, a one- dimensional how model was used as a diagnostic tool to calculate Nu and Sh numbers from experimental data Three different mathematical models were assembled. The only model which was entirely consistent with experimental results was the one-dimensional model which incorporated intrinsic chemical kinetics, intraphase diffusion resistance and employed Sherwood and Nusselt numbers attributable to laminar how in channels for the assessment of interphase resistances.