A sheet-processing machine contains at least one processing station in the form of a printing unit, and a delivery with an endless conveyor and after-grippers that are guided by a mechanism connected to a drive. The after-grippers take over the processed sheets from the endless conveyor and release them over a stack. The sheet-processing machine provides for it to be possible for the mechanism to be set to positions that are correlated with different formats of the processed sheets, and for the drive that actuates the mechanism to keep the mechanism at one and the same phase angle with respect to the printing unit in each of the positions. Therefore, even in the event of different formats of the processed sheets, user-friendly placing of the stack is possible.