Abstract: In order to so improve a machine for the non-circular machining of workpieces comprising a machine frame, a workpiece spindle held on the machine frame for receiving a workpiece and having a C-axis sensor, a Z-slide displaceable parallel to the workpiece spindle and having a Z-axis sensor, an X-axis drive arranged on the Z-slide for advancing a tool towards the workpiece, an X-axis sensor for determining the position of the tool, and a control device, that it operates quickly and reliably, it is proposed that the control device comprise a numerical machine control system for activating the workpiece spindle and the Z-axis drive and include a numerical X-axis control system, that the X-axis control system activate the X-axis drive independently of the machine control system in accordance with the predetermined non-circular shape, and that a coordination take place between the machine control system and the X-axis control system after certain time intervals.