The present invention is an EDM (Electrical discharge machining) process and apparatus for machining an electrode workpiece by means of an electrode tool wherein the electrodes are displaced relative to each other along a principal feed axis while, simultaneously, the electrodes are displaced relative to each other along an orbital path in a plane perpendicular to the principal feed axis, such as to produce between the electrodes a three-dimensional translation motion, and for providing between the electrodes an average machining gap wider than the gap width sustaining electrical discharges. The invention provides a control of the amplitude of the relative translation motion of the electrodes while displacing the direction of said motion as soon as a predetermined orbiting path limit is reached such as to allow a rapid increase of the gap between the electrodes when the electrode tool is retracted.