The reactions H + O-2 (+M) -> HO2 (+M) and H + OH (+M) -> H2O (+M) have been studied using high-level quantum chemistry methods. On the basis of potential energy hypersurfaces obtained at the CASPT2/aug-cc-pVTZ level of theory, high-pressure limiting rate coefficients have been calculated using variable reaction coordinate transition state theory. Over the temperature range 300-3000 K, the following expressions were obtained in units of cm 3 molecule(-1) s(-1); k(infinity)(H + O-2) = (25T(-0.367) + (7.5 x 10(-2))T-0.702 x 10(-11) and k(infinity)(H + OH) = (4.17 x 10(-11))T(0.234)exp(57.5/T). Available experimental data on the pressure dependence of the reactions were analyzed using a two-dimensional master equation. The following low-pressure limiting rate coefficients were obtained over the temperature range 300-3000 K in units of cm 6 molecule(-2) s(-1): k(0)(H + O-2 + Ar) = (9.1 x 10(-29))T(-1.404)exp (-134/T), k(0)(H + O-2 + N-2) = (2.0 x 10(-27))T(-1.73)exp (-270/T), k(0)( H + OH + Ar) = (8.6 x 10(-28))T(-1.527)exp (-185/T), and k(0)(H + OH + N-2) = (1.25 x 10(-26))T(-1.81)exp (-251/T). For the H + O-2 reaction system, F-cent(Ar) = 0.67 and F-cent(N-2) = 0.72 were obtained as center broadening factors, whereas F-cent(Ar) = 0.72 and F-cent(N-2) = 0.73 were obtained for the H + OH reaction system. The calculations provide a good description of most of the experimental data, except the room temperature measurements on the H + OH (+M) -> H2O (+M) reaction.