Several ab initio studies have focused on the minimum energy path region of the hydroperoxyl potential energy surface (PES) [J. Chem. Phys. 88, 6273 (1988)] and the saddle point region for H-atom exchange via a T-shaped HO2 complex [J. Chem. Phys. 91, 2373 (1989)]. Further, the results of additional calculations [J. Chem. Phys. 94, 7068 (1991)] have been reported, which, when combined with the earlier studies, provide a global description (but not an analytic representation) of the PES for this reaction. In this work, information at the stationary points of the ab initio PES is used within the framework of conventional Transition State Theory (TST)/RRKM. Theory to compute estimates of the thermal termolecular rate coefficients for the reaction between the H(D) atom and O-2 in the presence of two different bath gases, argon and nitrogen, as a function of pressure and temperature. These calculations span a pressure range from 1.0 Torr to the high-pressure limit and a temperature range from 298.15 to 6000.0 K. Conventional TST/RRKM Theory was utilized within the framework of two models : an equilibrium model employing the strong collision assumption (model I), [R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions (Blackwell, Oxford, 1990), as implemented in the UNIMOL program suite]; and a steady-state model that includes chemical activation (model II), using the collisional energy transfer approximation proposed by J. Tree [J. Chem. Phys. 66, 4745, 4758 (1977); 97, 288 (1992)]. In this work we first summarize the pressure-dependent fall-off curves (calculated with model I) and the high-pressure limit rate coefficients (Calculated with models I and II) over the entire temperature range, and then focus on the fall-off behavior for temperatures between 298.15 and 2000.0 K. Direct comparisons are made between the experimentally determined termolecular rate coefficients (either from direct measurements or based on recommended pressure/temperature-dependent expressions) and the estimates of these rate coefficients calculated in this work as a function of pressure at 298.15 and 500.0 K. In the fall-off region, we find better agreement between the theoretical and experimental values at low pressures than at pressures approaching the high-pressure limit. Significant deviations are observed between theory and experiment as the high-pressure limit is approached. The disagreement at 298.15 K is greater for N-2 than for Ar.