Abstract: In a two-axis turning machine, the cutting tool unit machines a first diameter of a workpiece portion of barstock extending from a main spindle chuck. A special subspindle chuck rotating in the same direction advances axially, grasps the workpiece as it is cut off from the barstock, and retracts. The barstock is fed through the first chuck for subsequent first operation machining and located against a stop which is independent of the tool slides. The subspindle chuck rotation is reversed, displacing the first-generated workpiece axis from the subspindle axis, and a second diameter, eccentric to the first diameter, is formed by the cutting tool unit in a second operation.