Semiconductor wafers are produced from a workpiece by means of a wire saw, by feeding the workpiece through an arrangement of wires tensioned between wire guide rollers and divided into wire groups, the wires moving in a running direction producing kerfs as wires engage the workpiece. For each of the wire groups, a placement error of the kerfs of the wire groups determined, and for each of the wire groups compensating movements of the wires of the wire group are induced as a function of the placement error, in a direction perpendicular to the running direction of the wires during feeding of the workpiece through the arrangement of wires, by activating at least one drive element.