Hydrogen abstraction from a molecule by OH is an important step in several reaction mechanisms of a key relevance in the chemistry of the atmosphere. The upper limit at 300 K for the rate constant of one of the simplest hydrogen abstraction reactions, HO + HOH --> HOH + OH (1), has been experimentally established. This reaction is intrinsicaly interesting because the associated isotope exchange reactions, (HO)-O-18 + HOH --> (HOH)-O-18 + OH (2) and DO + HOH --> DOH + OH (3), could affect the isotopic composition of the stratospheric water. The rate constants for those two reactions have also been experimentally measured in the interval 300-420 K (reaction 2) and at 300 K (reaction 3). In addition, the upper limit at 300 K for the rate constant of the reaction HO + DOD --> HOD + OD (4) has also been given. In this paper, we have theoretically calculated the rate constants and their temperature dependence for the above-mentioned four hydrogen (deuterium) transfer reactions by means of ab initio electronic structure calculations on their corresponding potential energy surfaces, followed by dynamical calculations based on the canonical unified statistical theory (CUS). The only available experimental activation energy (4.2 +/- 0.5 kcal/mol for reaction 2 over the range 300-420 K) is in very solid agreement with our theoretical Value of 4.27 kcal/mol obtained from first principles. In addition, our results confirm the experimental finding that these reactions have preexponential factors clearly lower than other typical hydrogen abstractions by HO. These low values for the two Arrhenius parameters come from a noticeable curved theoretical Arrhenius plot that, in turn, is a consequence of the large tunneling effects present in all these hydrogen (deuterium) abstraction reactions. No curvature was detected in the experimental Arrhenius plot for reaction 2, due to the small temperature range studied (300-420 K). The main cause for such large tunneling effects is the existence of an association complex, in which the two reactants are hydrogen bonded, which forms before the abstraction process itself takes place. Then, the adiabatic energy profile (effective potential for the tunneling calculation) is much thinner than that in a more typical bimolecular hydrogen (deuterium) transfer reaction. Finally, the kinetic isotope effects have been calculated, and a comparison with experimental rate constants rations has also been made.