Abstract: The present invention relates to a machine tool which permits the machining of nonaxisymmetric surfaces on a workpiece while rotating the workpiece about a central axis of rotation. The machine tool comprises a conventional two-slide system (X-Y) with one of these slides being provided with a relatively short travel high-speed auxiliary slide which carries the material-removing tool. The auxiliary slide is synchronized with the spindle speed and the position of the other two slides and provides a high-speed reciprocating motion required for the displacement of the cutting tool for generating a nonaxisymmetric surface at a selected location on the workpiece.