Abstract: A process for producing stainless steels, particularly special steels containing chromium and chromium-nickel, in a smelting arrangement having at least two vessels, for supplying a steel foundry. A charge having mostly iron-containing raw scrap materials and partially carbon-containing alloy carriers is melted in a first vessel. At a temperature of 1460° C., the melt is decarburized by the injection of oxygen so as to reduce the carbon content to less than 0.3%. The melt is heated to a tapping temperature of between 1620° C. to 1720° C. and the carbon content is subsequently reduced to 0.1%. A second charge is melted in a second vessel simultaneously with the decarburizing of the first charge in the first vessel.