An oxygen storage material based on cerium oxide with at least one other oxide of the metals silicon and zirconium, wherein the cerium oxide and the other oxides are present in the form of a mixed oxide. The material is obtainable in that hydroxidic precursors of the mixed oxide are first prepared in a manner known per se using a wet-chemical route, these precursors are optionally dried at temperatures between 80 and 300° C. and the dried precursors are then treated under a hydrogen-containing atmosphere at a temperature between 600 and 900° C. for a period of 1 to 10 hours. The reductive thermal treatment endows the material with a greatly improved dynamic behavior as compared with conventional calcination in air.