Catalytic methane oxidation is used in exhaust gas after treatment to reduce methane emissions in stationary combustion processes as well as in natural gas vehicles. Pd/zeolite catalysts provide higher activity than the commonly used Pd/Al2O3, but suffer from rapid deactivation under reaction conditions and in the presence of steam. This work presents a detailed study of deactivation of 1 wt% Pd/H-ZSM-5 catalyst in reaction conditions in dry and wet feed including characterization of both the active phase and the support. Initially well-dispersed PdO particles are not stable and sinter immediately after the exposure to the reaction mixture even in dry feed and stabilize at lower dispersion level. Despite the reasonable methane oxidation activity exhibited by the large particles, the initial PdO particles could potentially provide a 40 degrees C lower methane oxidation temperature. In the presence of water in the feed at moderate temperature (450 degrees C), support degradation governs the deactivation of the catalyst, which is evidenced by a significant decrease in BET surface area and generation of extra-framework aluminium species. These results suggest that active and stable catalysts could be obtained by careful choice and design of the support material with the aim to guarantee high dispersion of PdO.