The effects of pressure, temperature, and quantum-mechanical tunneling on the formation of CO2 and H(D) atoms in the OH(OD) + CO reactions have been investigated by a multichannel RRKM calculation using the potential energy surface obtained by various high-level computational techniques including the G(2) and modified G2 (G2M) methods. The strong non-Arrhenius behavior of the bimolecular rate constant for the OH + CO reaction was found to result from the combination of temperature, pressure, and quantum-mechanical tunneling. The effects of the latter two factors dominate at low temperatures, resulting in the significant leveling-off of the Arrhenius plot, The rapid increase in the rate constant above 1000 K was found to result from the sharp increase in the vibrational partition function of the transition state leading to CO2 product formation. The observed strong isotope effect (k(H)/k(D)) can also be reasonably accounted for by the combined T, P and tunneling effects. The absolute values of the total rate constant were found to be controlled primarily by the barrier heights at TS I and TS2 for the formation of HOCO and H + CO2 products, respectively, and independent of the two weakly bound van der Waals precursor complexes, OHOC and OHCO. The barriers, which account best for the bulk of experimental data are 0.8 and 2.0 kcal/mol, respectively, within the ranges of our predicted values 1.0 and 2.3 kcal/mol based on different methods with about I (or +/- 0.5) kcal/mol spread in the values.