Abstract: The object of the invention is a corrosion-resistant composite wire with diameters <10 mm, which has a concentric, homogeneous high-grade steel coating, wherein this coating, depending on the diameter of the wire and the application, can vary 15-30% by volume, and its strength can vary, depending on the core wire used and the degree of forming, up to .ltoreq.2000 N/mm.sup.2. To produce such a composite wire, for example, a high-strength, patented and surface-pretreated steel wire is sheathed with a strip of high-grade steel. In the first forming step, the longitudinally welded high-grade steel sheath is pressed tightly onto the core wire and in subsequent drawing steps, the composite wire is drawn to the final dimensions. At least between two forming steps, there is a selective annealing treatment of the composite wire by means of a rotary arc, whereby only the high-grade steel layer is heated to the annealing temperature.