Nanoscale corundum powders are obtained by first producing an Al2O3 precursor by adding seed crystals to an aqueous solution of an aluminium compound and adding a base and then converting the Al2O3 precursor into corundum by calcination at a high temperature. Before the calcination, the salts that are present in addition to the Al2O3 precursor are separated off. The resulting product is calcined at temperatures of 700 to 975° C. and any fines that may be present are removed. The resulting corundum powders can be sintered at temperatures of ≦1200° C. to produce compacts or components of multiple layer systems.