A process is disclosed for cooling molten steel, in particular by continuous casting of hoop-steel. At least part of the molten mass that leaves a metallurgical vessel through a metal nozzle solidifies when contacting a cooling surface. According to the invention, a gaseous stream that forms a reducing atmosphere is directed onto the surface of the freely accessible liquid hoop-steel immediately after it leaves the metal nozzle and the surface of the hoop-steel is exposed to this gaseous atmosphere at least until it is completely solidified.
