is transversable in the direction of the double arrow x the electrode holder 9 which is linearly moveable in the tool slide 8 is capable of performing a linear oscillation double arrow z osz and a linear vertical feed double arrow z vor which superimposes the linear oscillation and for this purpose is also connected to a third and fourth drive 10 effecting the linear feed and the linear oscillation movement horizontal feed of the tool slide 8 is effected by a fifth drive the operation of the above apparatus and the inventive method performed by means of this apparatus are explained as follows by way of the example of the manufacture of a one piece compressor rotor wheel blisk of an engine in connection with the fig1 to 8 in a first process step a sample workpiece 12 here a compressor rotor wheel with circumferentially arranged blades 12 a is produced from an inexpensive electrically conductive material using a conventional machining process for clarity fig1 to 8 show only part of the tool or workpiece with three blades 12 a each depending on the size of the component to be manufactured and the capacity of the pem equipment available the sample workpiece 12 can be a complete model of the final component such that the complete component is machined simultaneously or can only be a portion for example.