An NC EDM process and apparatus, where a sequence of electrical discharges is performed in an EDM working gap for the electroerosive removal of material from the workpiece, while the tool electrode is fed relatively in succession into the workpiece under NC commands which in a predetermined set establish a desired path and a desired size of the relative feed. The EDM current supply (generator) is controlled in such a way that the parameters of the electrical discharges are held in a predetermined EDM mode of operation during an initial period of the successive feed of the tool electrode relative to the workpiece. The occupying of a position of the tool electrode relative to the workpiece, at a predetermined distance from its final position, which is determined by the size of the successive relative feed, is detected for changing over the parameters of the electrical discharges into another EDM mode of operation and for maintaining the changed-over parameters until the tool electrode occupies the end position relative to the workpiece.
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