The kinetics of the catalytic combustion of methane by supported palladium oxide catalysts (2 wt.-% Pd/La2O3 . 11Al(2)O(3) and 5 wt.-% Pd/gamma-Al2O3) were examined for several oxygen partial pressure levels over the temperature range from 40-900 degrees C using temperature-programmed reaction and slow ramp and hold temperature-time transient techniques. Combustion rates were measured by differential reaction in a fixed bed of powdered catalyst at lower temperatures (200-500 degrees C). Also, by preparing the catalysts as thin (ca. 10 mu m) coatings on an alumina tube and conducting the experiments with very high flows of dilute methane and oxygen in helium, the rate measurements were extended up to 900 degrees C without significant contribution from gas phase reactions. The specific combustion activity of supported PdO shows a persistent hysteresis between 450 and 750 degrees C, i.e., the rate of combustion between these temperature limits depends strongly on whether the catalyst is cooling from above 750 degrees C or heating from below 450 degrees C. This region is also notable for negative apparent activation energy in the rate of methane oxidation, i.e., the rate increases with decreasing temperature during reoxidation of the Pd metal and decreases with increasing temperature (especially with low oxygen partial pressure) prior to decomposition of the bulk oxide. Detailed time-temperature transient kinetic analyses were performed for supported PdO catalysts within the 450-750 degrees C temperature range. The hysteresis in methane combustion rate is caused by a higher activation energy for reduction of oxygen chemisorbed on metallic Pd and by suppressed reoxidation of Pd metal relative to PdO decomposition.