Oxygen is a critical control variable for composting and other solid-state biodegradation processes. In this study we examined the effect of varying oxygen concentrations (1%, 4%, and 21% O2 (v/v)) on biodegradation kinetics under different substrate (sewage sludge and synthetic food waste), temperature (35, 45, 55, and 65 degrees C), and moisture (36-60% H2O) conditions. Three forms of a saturation or Monod-type model and one form of an exponential model were evaluated against data from extensive experiments under carefully controlled environmental conditions. The exponential model performed well at temperatures from 35 to 55 degrees C but had problems at higher temperatures. The Monod-type models yielded the best fit based on R2 values. Multiple linear regression was used to express the oxygen half-saturation coefficient as a function of temperature and moisture. For a modified one-parameter saturation model the half-saturation coefficient varied from -0.67% to 1.74% v/v O2 under the range of conditions typical of composting systems. While the positive correlation of biodegradation rate with oxygen concentration reported by previous researchers held true for temperatures below 55 degrees C, an inverse relationship was found at 65 degrees C. Although this study did not directly examine anaerobic conditions, the results under microaerophilic conditions suggest oxygen may not offer kinetic advantages for extreme thermophilic biodegradation processes.