A method and a grinding machine to implement the method includes, in a single clamping, a machine part is ground. The part is clamped on its ends and has an internal recess for grinding. The internal recess is ground with an internal grinding wheel, wherein the part is rotated between a workpiece headstock and a tailstock, and an external contour is ground by means of a grinding wheel. The part is held on the tailstock by a hollow tailstock sleeve, on the end region of the internal recess, and the internal grinding wheel passes through the hollow tailstock sleeve during grinding. In the grinding machine, a separate grinding spindle head carrying the internal grinding wheel can be included in the region of the tailstock, and can be advanced against the peripheral surface of the internal recess by passing through the hollow tailstock sleeve and the hollow center.
