An existing, validated elementary reaction model for hydrogen oxidation in supercritical water, with theoretically consistent modifications for high pressure, was expanded to allow modeling of carbon monoxide oxidation. The carbon monoxide model was less successful, exhibiting a higher overall activation energy than the data and lacking an oxygen dependence. Data for fuel-rich CO oxidation, including hydrogen formation, were well predicted, but results for fuel-lean conditions were not correctly predicted. Both models, when extended to subcritical conditions, successfully reproduced the majority of the experimentally observed pressure (water-density) dependence. The primary effect of the high water density on oxidation kinetics is the increase in the rate of the HO2 + H2O --> H2O2 + OH reaction, which is effectively a branching step; the dissociations of hydrogen peroxide (H2O2) and the hydroperoxyl radical (HO2) are also at or near their high-pressure limits. The increase in the rate of the branching reaction with increasing water density accounts for the majority of the oxidation pressure dependence. The models for hydrogen and carbon monoxide oxidation exhibited high sensitivities to the rate constant and equilibrium constant for the branching reaction, and experimental data could be reproduced only if the value of this rate constant in supercritical water is significantly lower than its most probable value based on gas-phase measurements.