Abstract: The present invention is a process and apparatus for machining an electrode workpiece by electrical discharges, wherein the electrode workpiece and an electrode tool are displaced relative to each other at least in one slant direction disposed at a predetermined angle with the principal axis of feed of one electrode relative to the other, the machining gap between the electrodes is set at a finite value such as to maintain predetermined machining conditions, consecutive machining passes are effected and, at the end of each machining pass, the slant direction of feed is displaced as soon as the amplitude of relative displacement between the electrodes reaches a predetermined limit value, and such limit value is changed from one pass to the next.