Rate constants for the isotope exchange reactions of OH- with D-2 and OD- with H-2 have been measured as a function of average center-of-mass kinetic energy at several temperatures. The reaction of OH- with D-2 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 D-2 rotational temperature was found. The reason for this dependence is unclear at present. In contrast, the reaction of OD- with H-2 is slightly endothermic and shows positive dependences on both temperature and kinetic energy. The negative rotational dependence for the reaction of OD- with H-2 is not as large as that for OH- + D-2, presumably because rotational energy can help overcome the endothermicity in the case of OD- + H-2. Vibrational energy is observed to promote reactivity in both reactions.