A process for preparing zirconium-cerium-based mixed oxides which comprises reacting an alkali with an aqueous solution of a zirconium salt containing 0.42-0.7 mole of sulphate anion (SO.sub.4.sup.2-) per mole of zirconium cation at a temperature of not greater than 50.degree. C., in the presence of a cerium salt to form a cerium-zirconium mixed hydroxide, and then calcining the cerium--zirconium mixed hydroxide to form a mixed oxide. The mixed oxides possess good thermal stability and are essentially single phase and are suitable as promoters and catalyst supports in, particularly, automobile exhaust systems.