Method for the electroslag refining of metals of which at least 50 weight-percent are in the form of at least one current-carrying consumable electrode, especially one having alloy components with an affinity for oxygen, wherein the metals are remelted to an ingot through a molten bath of slag. To achieve the object of preventing oxidation, freckling, rings and white spots and at the same time produce a degassing, the following measures are undertaken: (a) the refining process is performed at a subatmospheric pressure, (b) the slag is an at least 80 weight-percent oxidic slag of oxides whose boiling points are above 2000.degree. C., and (c) the slag is heated by means of alternating current.