Nonstoichiometric Ba beta-alumina single crystals, Ba1-0.25xMg1-xAl10+xO17+0.25x (0 less than or equal to x less than or equal to 1), were prepared in the BaO-MgO-Al2O3 system by a floating zone method. The single crystals were cleaved parallel to a (001) plane. The electrical conductivity parallel to the cleavage plane (sigma(//)) was 10 to 20 times greater than that perpendicular to the cleavage plane (sigma(perpendicular to)). The sigma(//) and sigma(perpendicular to) had the maximum at around x = 0.5. The activation energy of sigma(perpendicular to), 240 to 270 kJ/mol, was slightly greater than that of sigma(//), 170 to 190 kJ/mol. The sigma(//) was almost independent of oxygen partial pressure (P-O2), while sigma(perpendicular to) showed a P-O2(-1/6) dependence in a low P-O2 region of P-O2 = 10(-4) to 10(-13) Pa. (C) 2003 Elsevier B.V. All rights reserved.