Rate constants for the isotope exchange reactions of OH− with D2 and OD− with H2 have been measured as a function of average center-of-mass kinetic energy at several temperatures. The reaction of OH− with D2 is slightly exothermic, and the rate constant has a negative temperature dependence. The kinetic energy dependences of the rate constants have minima near 0.1 eV. A strong negative dependence on the D2 rotational temperature was found. The reason for this dependence is unclear at present. In contrast, the reaction of OD− with H2 is slightly endothermic and shows positive dependences on both temperature and kinetic energy. The negative rotational dependence for the reaction of OD− with H2 is not as large as that for OH−+D2, presumably because rotational energy can help overcome the endothermicity in the case of OD−+H2. Vibrational energy is observed to promote reactivity in both reactions.