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 strategy 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;4) resumption of wire-part relative movement, with the new parameter value over a computer predetermined distance, and5) variation of the parameter in the opposite direction so as to return it to its initial value.The step durations are slaved to changes of a factor giving an image of the conditions existing in the machining slot, around a predetermined threshold.