Three compounds have been found to be stable in the pseudobinary system Na2O-(alpha)Al2O3 between 825 and 1400 K; two nonstoichiometric phases, beta-alumina and beta"-alumina, and NaAlO2. The homogeneity of beta-alumina ranges from 9.5 to 11 mol% Na2O, while that of beta"-alumina from 13.3 to 15.9 mol% Na2O at 1173 K. The activity of Na2O in the two-phase fields has been determined by a solid-state potentiometric technique. Since both beta- and beta"-alumina are fast sodium ion conductors, biphasic solid electrolyte tubes were used in these electrochemical measurements. The open circuit emf of the following cells were measured from 790 to 980 K: [GRAPHICS] The partial molar Gibbs' energy of Na2O relative to gamma-Na2O in the two-phase regions can be represented as: DELTA-GBAR(Na2O)(alpha- + beta-alumina) = -270,900 + 24.03 T, DELTA-GBAR(Na2O)(beta- + beta"-alumina) = -232,700 + 56.19 T, and DELTA-GBAR(Na2O)(beta"-alumina + NaAlO2) = -13,100 - 4.51 T J mol-1. Similar galvanic cells using a Au-Na alloy and a mixture of Co + CoAl(2+2x)O4+3x + (alpha)Al2O3 as electrodes were used at 1400 K. Thermodynamic data obtained in these studies are used to evaluate phase relations and partial pressure of sodium in the Na2O-(alpha) Al2O3 system as a function of oxygen partial pressure, composition and temperature.