Complex perovskites, of the types A(2)(B'B ")O-6 and A(3)(B'B-2")O-9, (in which A ions are always 2 +, B' ions are 3 + and 2 +, respectively, and B " ions are 5 +), can become good high-temperature protonic conductors when they are made nonstoichiometric by increasing the concentration of the B' ions at the expense of the B " ions. After heating in water vapor, uptake of H2O occurs, and protons enter the structure. We consider the effects of several variables on the bulk ionic conductivity and activation energy for protonic conduction, including degree of nonstoichiometry, the effect of ordering on the B-sites, the effect of varying the radius of the B' ion and the effect of changing the A ion from Sr2+ to Ba2+. The results show that disorder favors a higher conductivity, that the degree of order can change with nonstoichiometry, and that Ba compounds always have higher conductivity and lower activation energy than the corresponding Sr compounds.