The electrical conductivity change with annealing at 1000 degrees C in the Yb2O3-ZrO2 (YbSZ) and Sc2O3-ZrO2 (ScSZ) systems have been examined. The conductivity change depended on the composition of the dopant. In the YbSZ system, the sintered sample with 10 mol% Yb2O3 showed only slight conductivity decrease with annealing, while those with 8 mol% Yb2O3 and 12 mol% Yb2O3 a significant decrease. The ScSZ with 8 mol% Sc2O3 (88cSZ) exhibited the cubic phase and those with 11 and 12 mol% Sc2O3 (11ScSZ and 12ScSZ) the rhombohedral phases at room temperature. 8ScSZ showed a significant aging effect with annealing at 1000 degrees C. 11ScSZ and 12 ScSZ showed no conductivity change with annealing.