Mixed oxides excellent in thermal stability of specific surface area and in oxidation-reduction performance are provided on an industrial scale. Catalyst materials useful in exhaust gas purification are also provided. The invention is concerned with mixed oxides containing cerium, zirconium and sulfur, namely cerium- and zirconium-based mixed oxides having the composition: 50 to 79% by weight as cerium oxide, 20 to 49% by weight as zirconium oxide, and 1 to 5% by weight as sulfate (SO.sub.4). The invention also relates to a method of producing cerium- and zirconium-based mixed oxides which comprises mixing a cerous-alkali metal sulfate double salt with a zirconium ion-containing solution and then adding a base to the mixed solution to thereby cause formation of a precipitate. The invention further relates to catalyst materials for exhaust gas purification which comprise a mixed oxide containing cerium, zirconium and sulfur, namely a cerium- and zirconium-based mixed oxide containing sulfur in an amount of 0.5 to 5% by weight as sulfate (SO.sub.4).