Polycrystalline cerium oxide powder in the form of aggregates of primary particles with a specific surface of between 70 and 150 m.sup.2/g, an average primary particle diameter of between 5 and 20 nm and an average, projected aggregate diameter of between 20 and 100 nm. It is produced in that an aerosol is reacted in a flame obtained from a hydrogen-containing combustible gas and primary air and the solid obtained is then separated from the gaseous substances.