Spark erosion machining processes and machines are claimed in which three-dimensional control is effected by NC regulation while carrying out advance in a Z-axis direction for compensating electrode length wear and X-Y plane advance to machine a desired three-dimensional shape. One process involves (a) storing a compensating movement amount for carrying out a correction in the Z-axis direction corresponding to a determined unitary movement distance in a X-Y plane; and (b) carrying out an advance, according to the determined compensating movement amount, in the Z-axis direction every time that a movement distance in the X-Y plane attains the unitary movement distance.