An arrangement for detecting abnormal concentration of electrical discharges between a travelling wire electrode and a workpiece in a travelling wire EDM apparatus. The abnormal electrical discharge detector of the invention comprises a circuit measuring the voltage across a pair of contacts supplying machining current to the electrode wire. The length of the electrode wire between the two contacts forms a pair of variable resistors connected in a branch of a Wheatstone bridge circuit. The voltage measuring circuit, connected across a diagonal of the bridge, in turn controls some of the machining parameters such as to prevent damages, as for example rupture of the wire electrode, when an abnormal concentration of electrical discharges is detected at a given point of the machining zone between the wire electrode and the workpiece.