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Using the method of the joint crystallization of solutions of nitrate salts with ultrasonic treatment, xerogels and highly dispersed mesoporous powders of the following composition are synthesized: (CeO2)1 – x(Nd2O3)x (x = 0.02; 0.05; 0.10), Gd1 – xSrxCo0.5O3 – δ (x = 0.1, 0.15, 0.2, 0, 25), Gd0.4Sr0.1Ni0.5O3 – δ, and Gd0.125La0.125Sr0.25Co0.5O3 – δ; and based on them, nanoceramic materials with a crystalline cubic structure of the fluorite type, as well as an orthorhombic and tetragonal structure of the perovskite type with CSR ~ 55–90 nm (1300°С), respectively, are obtained. The physicochemical properties of the resulting ceramics are studied; it is revealed that it has an open porosity of 7–11% for the composition (CeO2)1 – x(Nd2O3)x and 17–42% for materials with the Gd1 – xSrxCo0.5O3 – δ, Gd0.4Sr0.1Ni0.5O3 – δ, and Gd0.125La0.125Sr0.25Co0.5O3 – δ composition. Materials based on cerium oxide predominantly have the ionic (ion transport numbers ti = 0.71–0.89 in the range 300–700°С) type of electrical conductivity due to the formation of mobile oxygen vacancies in the heterovalent substitution of Ce4+ by Nd3+; and σ700°С = 0.31 × 10–2 S/cm Solid solutions based on nickelate and lanthanum cobaltite have mixed electron-ionic conductivity, σ700°С = 0.59 × 10–1 S/cm with transfer numbers te = 0.92–0.99 and ti = 0.08–0.01. The prospects for using the obtained ceramic materials as solid oxide electrolytes and electrodes for medium-temperature fuel cells (FCs) are shown. [ABSTRACT FROM AUTHOR]