Mechanistic details of CH4 oxidation were examined on PdO/ZrO2 catalysts using isotopic tracer methods and measurements of kinetic isotope effects. Normal kinetic isotope effects were observed using CH4/O-2 and CD4/O-2 reactant mixtures. The (k(H)/k(D)) ratio was between 2.6 and 2.5, and it decreased slightly as the reaction temperature increased from 527 to 586 K. These kinetic isotope effects reflect a combination of kinetic and thermodynamic effects, and the measured values are consistent with rate-determining C-H bond activation steps on surfaces predominantly covered with OH groups. Isotopic equilibration rates for CH4/CD4/O-2 mixtures were much lower than methane combustion rates, suggesting that C-H bond activation steps are irreversible on PdO at 473-600 K. Reactions of CH4/O-18(2) mixtures on pd(16)O-(ZrO2)-O-16 led to the initial formation of (CO2)-O-16, followed by a gradual increase in the concentration of other CO2 isotopomers as lattice O-16 atoms are replaced by O-18 from O-18(2). The involvement of lattice oxygens in C-H bond activation steps is consistent with a Mars-van Krevelen redox mechanism. Reactions of CH4/O-16(2)/O-18(2) mixtures lead to all CO2 isotopomers without the concurrent formation of (OO)-O-16-O-18. Thus, dissociative oxygen chemisorption is also irreversible during methane combustion. Oxygen atoms in (CO2)-O-16 exchange with (PdO)-O-18-(ZrO2)-O-18 catalysts at temperatures lower than those required for methane combustion, suggesting that CO2 desorption is quasi-equilibrated. These mechanistic conclusions are consistent with the measured dependence of CH4 oxidation rates on O-2, CH4, H2O, and CO2 concentrations. The resemblance between the reaction kinetics on PdO/ZrO2 and on other supported PdO catalysts suggests that the mechanistic conclusions reached in this study are generally valid for methane combustion catalysts based on PdO.