Abstract: A method of and a spark erosion apparatus for fine machining by spark erosion of a workpiece (2) with a wire electrode (1) eliminates very efficiently process interruptions caused by short circuits, such that at least one gap parameter is continuously monitored for the purpose of detecting a short circuit; when a short circuit is detected, the forward motion of the electrode (1) is arrested at the point (K) where the short circuit occurred; if the short circuit persists, the electrode (1) is moved away from the workpiece (2) to an intervention point (M)--in a direction perpendicular to the path (6) used for trim cutting; at the intervention point (M), one or several measures to eliminate the short circuit are executed once or several times; and after it has been detected that the short circuit is eliminated, the electrode (1) is moved back to the point (K) where the short circuit occurred, whereafter normal machining continues.