The conductivities of sodium beta "-alumina ceramic in low pressure sodium vapor and potassium beta "-alumina ceramic in low pressure potassium vapor have been characterized in the four-probe configuration by ac and de measurements. Porous Rh/W films deposited by a photolytic process on Na beta "-alumina and sputtered Mo films on K beta "-alumina were used as electrodes. Alkali vapor pressures from 0.1 to 3.0 Pa and ac signal amplitudes from 2 to 25 mV were used, with ohmic behavior observed under these conditions. Periodic interruptions of the high temperature stand were made to characterize conductivity of the solid electrolyte sample over several hundred kelvin. Conductivities dropped slightly for sodium beta "-alumina ceramic and similar to 30% for potassium beta "-alumina ceramic during the first 100 h of test; the conductivities were then stable over 1550 h at 1130 K for the Na beta "-alumina ceramic and rose slightly 495 h at 1200 K for the K beta "-alumina ceramic. The high temperature conductivities vs. temperature were characterized for the equilibrated ceramics from below 900 K to above 1200 K; both ceramics showed good fits to an Arrhenius equation obeying the Nernst-Einstein relation between resistivity and diffusion over 400 K, with activation energies of 0.07 eV for sodium beta "-alumina ceramic and 0.27 eV for potassium beta "-alumina ceramic.