Abstract: The invention relates to a method and apparatus for oxygen-cutting thick pieces of steel at high speed. In accordance with the invention an oxygen-cutting torch (30) held at a predetermined height above the piece (1) to be cut and a slot torch (20) comprising at least one blade nozzle (25) that travels inside the cut slot (1.3) are moved synchronously. The blade nozzle (25) emits at least one jet of heating and/or oxygen-cutting fluids through its leading edge to strike the heating edge of the slot where it combines with the jet of oxygen-cutting fluids emitted by the oxygen-cutting torch (30) to form a leading edge (1.4) of the slot having a profile in the form of a broken line.