We have investigated the oxide-ion conduction of anion-deficient double perovskites of the formula, Ba2BB'O-5.5 (B = Li, Na; B' = Mo, W, Te), in relation to the parent oxides, Ba2BB'O, (B = Ca). Powder XRD and Li-7/Na-23 MAS NMR spectra indicate that the oxygen vacancies are not ordered in the Ba2BB'O-5.5 oxides. Anion-deficient oxides show appreciably higher conductivities than the parent stoichiometric oxides. The highest oxide-ion conductivity of similar to 10(-2) S/cm at 700 degrees C in this series is exhibited by Ba2NaMoO5.5. A smooth conductivity transition around 350 degrees C as indicated by a discontinuity in the Arrhenius plots of the molybdenum compounds has been ascribed to a change-over from a two-dimensional to bulk (three-dimensional) oxygen vacancy migration in these oxides.