Abstract: At least one machining parameter of an electrode-wire EDM machine, cutting according to a predetermined trajectory, is varied when the electrode-wire reaches the apex of an angle or approaches an arc. The process consists of the following stages:1) calculation of the locations along the trajectory or path at which these variations must be started;2) stopping of relative electrode-wire movement and the work-piece, when the wire reaches one of these points;3) gradual and stepped variations of the parameter up to a final designated value or until a predetermined number of steps have been performed, or during a given period of time;4) resumption of wire-part relative movement, with the new parameter value over a computed predetermined distance, and5) variation of the parameter in the opposite direction so as to return it to its initial value.The durations of the steps are predetermined or correspond to cutting of predetermined lengths along the path.