Abstract: A method and apparatus for wire electroerosive cutting of a workpiece, the wire guided in a toroidal guide and a main guide associated with the toroidal guide, the position(s) of the toroidal guide and/or of the main guide with respect to the desired position of the erosion wire is(are) calculated in real time, considering the geometry of the contour to be cut and of the instantaneous erosion parameters.

Abstract: To eliminate short-circuits between a countersink electrode and a workpiece during countersink erosion, when a short-circuit occurs, the countersink electrode is initially moved back by a predetermined path length (.delta.) along the previously travelled path from a first locus (P.sub.K) at which the short-circuit occurred to a second locus or intermediate point (P.sub.R) and it is established at that location whether there is still a short-circuit. If this is the case, the countersink electrode is moved in an upwardly sloping manner along a second path (R), which has a first angle (.alpha.) with respect to the working plane (AE) and has a movement component (R.sub.1) having a second angle (.beta.) with respect to a surface normal to the short-circuit or intermediate point (P.sub.K or P.sub.R). All the parameters (.alpha.,.beta.,.delta.,.vertline.R.vertline.) can be freely preselected and are variable during erosion.