Abstract: A process finishes the surface of rotationally symmetrical workpieces. The workpiece is pre-machined and hardened with a stock allowance and is then finished in two steps in a device in which it is clamped only once. The largest part of the stock allowance is first cut by a hard turning process and the residue is then ground down to the actual size of the workpiece to be manufactured. The device for performing this process includes a motor-driven workpiece spindle for receiving the workpiece having a spindle head. The workpiece spindle has at least one motor-driven grinding spindle adapted to accept a grinding tool. The grinding spindle generally is axially aligned with the workpiece spindle or the workpiece thereon. The workpiece spindle can be fitted with a lathe tool having a cutting edge for hard turning.