The effect of high-temperature aging for 4800 h at a temperature of 1123 K on the crystal structure and the conductivity of (ZrO2)0.90(Sc2O3)0.09(Yb2O3)0.01and (ZrO2)0.90(Sc2O3)0.08(Yb2O3)0.02single-crystal membranes were studied. Such membrane lifetime testing is critical to the operation of solid oxide fuel cells (SOFCs). The crystals were obtained by the method of directional crystallization of the melt in a cold crucible. The phase composition and structure of the membranes before and after aging were studied using X-ray diffraction and Raman spectroscopy. The conductivities of the samples were measured using the impedance spectroscopy technique. The (ZrO2)0.90(Sc2O3)0.09(Yb2O3)0.01composition showed long-term conductivity stability (conductivity degradation not more than 4%). Long-term high-temperature aging of the (ZrO2)0.90(Sc2O3)0.08(Yb2O3)0.02composition initiates the t″ → t′ phase transformation. In this case, a sharp decrease in conductivity of up to 55% was observed. The data obtained demonstrate a clear correlation between the specific conductivity and the change in the phase composition. The (ZrO2)0.90(Sc2O3)0.09(Yb2O3)0.01composition can be considered a promising material for practical use as a solid electrolyte in SOFCs.