We report on a study of the vibrational energy relaxation and resonant vibrational (Förster) energy transfer of the OD vibrations of D2O and mixtures of D2O and H2O using femtosecond mid-infrared spectroscopy. We observe the lifetime of the OD vibrations of bulk D2O to be 400 ± 30 fs. The rate of the Förster energy transfer is measured via the dynamics of the anisotropy of the OD vibrational excitation. For a solution of 0.5% D2O in H2O, resonant energy transfer is negligible, and the anisotropy shows a single exponential decay with a time constant of 2.6 ± 0.1 ps, representing the time scale of the molecular reorientation. With increasing concentration, the anisotropy decay becomes faster and non-exponential, showing the increased contribution of resonant energy transfer between the OD vibrations. We determine the Förster radius of the OD vibration of HDO in H2O to be r0 = 2.3 ± 0.2 Å.