The ionic conductivity of cubic solid solutions in the systems of CaO-$ZrO_2$, $Y_2O_3-ZrO_2$ prepared by SHS was examined. The higher conductivity appears to be related to a lower activation energy rather than to the number of oxygen vacancies dictated by composition. Conductivity-temperature data was obtained at 1000 $^{circ}C$ in atmosphere of low oxygen partial pressure (~$10^{-40}$ atm) for $Y_2O_3-ZrO_2$ cubic solid solutions. The data indicated that these materials could be reduced, and the decree of reduction would be related with the measuring electric field.