The reactions H + O2 (+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 + O2) = (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): k0(H + O2 + Ar) = (9.1x10(-29)) T(-1.404)exp (-134/T), k0(H + O2 + N2) = (2.0x10(-27)) T(-1.73)exp (-270/T), k0(H + OH + Ar) = (8.6x10(-28)) T(-1.527)exp (-185/T), and k0(H + OH + N2) = (1.25x10(-26)) T(-1.81)exp (-251/T). For the H + O2 reaction system, F(cent)(Ar) = 0.67 and F(cent)(N2) = 0.72 were obtained as center broadening factors, whereas F(cent)(Ar) = 0.72 and F(cent)(N2) = 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.