In a process for continuously melting scrap (6) and/or pig iron within a converter (1), the converter (1) is heated in proximity of the bottom (3) with sub-stoichiometric burners (4), having their flames (5) essentially radially directed into the interior of the converter (1). In this case, secondary air or O.sub.2 is supplied at a distance above the burner plane for the purpose of completing the combustion. The melt is, optionally together with slag, discharged via a tapping means (9) laterally connected to the converter (1) into a mobile ladle (19). For the purpose of interchanging ladles (19), the converter (1) is swivelled into a position in which the level of the melt is located below the taphole (11).