The rhombohedral alkaline earth-bismuth oxide phase, an oxygen ion conductor, does not coexist stably with electronic conductors in any of the three binary systems, Ca-Bi-O, Sr-Bi-O, Ba-Bi-O. A thermodynamically stable composite of a rhombohedral phase that contains Ba and Sr or Ca or both with the electronic conductor BaBiO 3 may be synthesized. The rhombohedral phase appears to have complete mutual miscibility of the alkaline earth elements. The compositions of rhombohedral phase that coexist with BaBiO 3 in the Sr-Ba-Bi ternary system and the CaSr-Ba-Bi quaternary systems are described. The value of ionic conductivity of the rhombohedral phase (at a constant Bi: [Ca+Sr+Ba]) is not dependent on the relative amounts of Ca, Sr, and Ba. The temperature at which the rhombohedral phase undergoes a polymorphic transformation from a low-temperature (β 2 ) form that is a weak ion conductor to a high-temperature (β 1 ) form that is a much better oxygen ion conductor. The temperatures of the polymorphic transformation and of the upper stability limit of the rhombohedral phase both depend strongly on Ca: Sr: Ba. The β 1 form develops in the Ba-Bi system at the lowest temperatures and at the highest ones in the CaBi system. On the other hand, the Ca-Bi phase has greater thermal stability than its Ba analogues. The temperature range over which a useful composite conductor can operate is, therefore, strongly dependent upon the bulk composition of the system.