The influence of the reaction parameters including temperature, oxygen concentration, and of in situ hydrogen reduction on the Pd catalyst activity towards complete methane oxidation is studied experimentally. Zero porosity alpha-alumina plates are used as a support for Pd catalyst. This lowers the influence of metal-support interaction on the catalyst state as confirmed by UV-visible spectroscopy. A plug flow reactor with a high linear gas velocity is used to measure the reaction rate. Overall conversion is kept low for most of the experiments so that the reaction is in the kinetically limited regime. The oxidation state of the catalyst before and after the reaction is determined using UV-visible reflectance spectroscopy of the plate surface. Changes in the catalyst activity with time are monitored after stepwise changes in the reaction parameters. Activity was found to decrease with time at low temperatures and high oxygen concentrations (condition when PdO phase is stable) and to increase with time at high temperatures and low oxygen concentrations (conditions when Pd is stable). A sharp increase in conversion was observed after the in situ hydrogen reduction of the sample. The experimental data is consistent with the reduced Pd form of the catalyst being more active towards methane oxidation than the oxidized PdO form at high temperatures. Possible particle size and morphology effects are discussed.