A conceptual picture is developed to explain the peculiar kinetic features of methane oxidation over supported Pd catalysts (observed by several investigators), notably the hysteresis in activity accompanying temperature cycles. Experiments were performed with supported Pd-catalysts to illustrate these features. The activity hysteresis is closely coupled with a hysteresis in oxygen content. The latter is in turn attributed to the properties of the PCT-diagram of the involved three-phase system; gas phase O-2 and the two solid phases, Pd and PdOx. The two main ingredients in the mechanism are : (i) the so-called absorption and decomposition "plateau" pressures for the O-2-Pd-PdOx system are different, i.e., show a hysteresis, (ii) these pressures are not independent of x, but increase with increasing oxygen content. Both features are deviations from the "ideal" three-phase system and are frequently observed for H-2-metalmetal hydride systems.