We have studied the influence of pressure and temperature on the detonability of hydrogen-air-diluent mixtures diluted with steam or carbon dioxide. Detonation cell width measurements have been obtained from experiments conducted in a 0.43-m-diameter heated detonation tube. Calculations from a Zeldovich-von Neumann-Doring (ZND) model of a detonation with a detailed chemical-kinetic reaction mechanism for hydrogen oxidation are used to correlate the data. The data show a significant reduction in the ability of a diluent (excess air or hydrogen, carbon dioxide, or steam) to inhibit a detonation as the temperature is increased from 293 to 373 K. Only a small decrease in the cell width is observed with increasing pressure between approximately 1 and 3 atm for hydrogen-air mixtures diluted with steam or excess air. For conditions beyond which data exist, calculations based on the model yield results that indicate similar detonabilities of all mixtures considered at low initial pressures or high initial temperatures. Additionally, these results indicate minima in the cell width for variations in the initial pressure and temperature. The cell minima represent approximately the location of a change in a rate-limiting mechanism corresponding to the extended classical second-limit criterion.