In a travelling wire EDM apparatus, the location of an electric discharge along the portion of the electrode wire in the machining zone between the electrode wire and the workpiece, in the course of a cut being effected on the electrode workpiece by electrical discharges, is measured by measuring the currents flowing through each of the two lines connecting one output of the pulse generator associated with the EDM apparatus to the electrode wire on one side and the other of the machining zone. The measured currents are added and subtracted and the position, or location, of an electrical discharge is determined by a signal proportional to the quotient of the difference by the sum of the currents.