Rate constants for the reactions (1) H + O2 --> OH + O and (2) D + O2 --> OD + O have been measured over the temperature ranges 1103-2055 K and 1085-2278 K, respectively. The experimental method that has been used is the laser photolysis-shock tube technique. This technique utilizes atomic resonance absorption spectrophotometry (ARAS) to monitor H- or D-atom depletion in the presence of a large excess of reactant, O2. The results can be well represented by the Arrhenius expressions k1(T) = (1.15 +/- 0.16) x 10(-10) exp(-6917 +/- 193 K/T) cm3 molecule-1 s-1, and k2(T) = (1.09 +/- 0.20) x 10(-10) exp(-6937 +/- 247 K/T) cm3 molecule-1 s-1. Over the experimental temperature range, the present results show that the isotope effect is unity within experimental uncertainty. The Arrhenius equations, k1(T) = (8.75 +/- 1.24) x 10(-12) exp(1121 +/- 193 K/T) cm3 molecule-1 s-1 and k2(T) = (9.73 +/- 1.79) x 10(-12) exp(526 +/- 247 K/T) cm3 molecule-1 s-1, for the rate constants of the reverse reactions were calculated from the experimentally measured forward rate constants and expressions for the equilibrium constants that have been derived from the JANAF thermochemical database. The theoretical implications of the present results are also discussed.