NOVELTY - Zirconium-hafnium mixed oxide powder (P1) in the form of aggregates of primary particles comprises zirconium dioxide (95-99.9 wt.%), hafnium dioxide (0.1-5 wt.%), carbon (0-0.15 wt.%), chloride (0-0.05 wt.%), where the sum of the proportions of zirconium dioxide and hafnium dioxide is at least 99.8 wt.%.    USE - For preparing dispersions; as filler; as support; as catalytically active substance; as dental material; in fuel cells; for producing membranes; as additive in silicone and rubber industry; for adjusting the rheology of liquid systems; for stabilizing heat shields; in paint industry; as colored pigment; and for producing piezoelectric materials (claimed).    ADVANTAGE - The zirconium-hafnium mixed oxide powder has a BET surface area of 60 plus minus 15 m2/g, average primary particle diameter of less than 20 nm, average aggregate surface area of less than 10000 nm2, average aggregate equivalent circle diameter of less than 100 nm, and average aggregate circumference of less than 700 nm. The zirconium-hafnium mixed oxide powder has the average maximum aggregate diameter of less than 150 nm and the average minimum aggregate diameter of less than 100 nm. The zirconium-hafnium mixed oxide powder has a compacted bulk density of 100 plus minus 20 g/l; a loss on drying of at most 2 wt.%, a loss on ignition of at most 3 wt.%, and a pH of 4 - 6, determined in a 4% aqueous dispersion.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for preparation of the zirconium-hafnium mixed oxide powder involving a solution containing as starting materials (obtained by mixing a solution containing at least one zirconium carboxylate, a hafnium carboxylate and/or a carboxylate displaying proportions of zirconium and hafnium in an organic solvent or organic solvent blend and a solution containing at least one zirconium alcoholate, a hafnium alcoholate and/or an alcoholate displaying proportions of zirconium and hafnium in an organic solvent or organic solvent blend, where the starting compounds are present in accordance with the desired ratio of zirconium dioxide and hafnium dioxide and in which weight ratio of carboxylate/alcoholate is 30:70 - 90:10), is atomized using an atomizing gas to form an aerosol; the aerosol is allowed to burn into a reaction chamber in a flame produced from a fuel gas (preferably hydrogen), and air (primary air), and air (secondary air) is additionally introduced into the reaction chamber (thus lambda1 as the ratio of oxygen present in the air used in total to oxygen to burn the fuel gas is 1.5 - 4 and lambda2 as the ratio of oxygen present in the air used in total to oxygen to burn the starting materials and the fuel gas is greater than or equal to 1 and lambda1 is greater than lambda2; and the residence time of the starting materials in the flame is 5 - 30 milliseconds); the hot gases and the solid products are cooled and the solid product is then separated from the gases.