What is described is a method and a grinding machine for implementing the method, in which a machine component (2) to be machined which is clamped at its two ends (3, 5) and has an internal recess (6) to be ground is ground in a single set-up. The internal recess (6) is ground by an internal grinding disc (8), wherein the machine component (2) is held so as to be rotationally driven in its set-up between a workpiece headstock (9) and a tailstock (10) and is additionally ground on its external contour (17) by means of a grinding disc (16). The machine component (2) is held in a centring manner on the tailstock (10) by a tailstock hollow sleeve (15) with a hollow centre (20) at the end region of the internal recess (6), wherein the internal grinding disc (8) engages through the tailstock hollow sleeve (15) and the hollow centre (20) during the grinding of the internal recess (6). In the case of the grinding machine according to the invention, a separate grinding headstock is preferably provided in the region of
