A device for machining a part by electrical discharge machining using an electrode wire. The device includes equipment for holding the electrode wire taut and driving the wire to translate longitudinally, in proximity to the part to be machined, in a sparking zone. The device further includes equipment for making a stream of dielectric liquid flow through the sparking zone between the electrode wire and the part to be machined. An electrical power source generates electrical pulses that cause sparks in the sparking zone between the electrode wire and the part to be machined. The quantity of gas bubbles present in the sparking zone is measured, and a signal is produced, representative of the quantity of bubbles, the signal being delivered to a controller. The controller modifies machining parameters so as to maintain the value of the signal within a suitable range.