During the operation of a delivery device, having a first and a second stack delivery, in a transport direction, in which a first braking device is provided in the transport path of sheets which are conveyed by a conveyor system along a transport path in the entry region of the first stack delivery, and in which a second braking device is provided in the input area of the second stack delivery, the sheets to be printed, which come into the first braking device come in a form- or friction-locking operative contact with an active surface of a holding means comprised by the braking device. The active surface coming into this operative contact with the sheet to be printed is moved forcibly by a drive in the transport direction. In a first operating mode, during a form- or friction-fit interaction between the sheet and the active surface, a speed for the movement of the active surface is reduced from a first speed to a comparatively lower stacking speed. The first braking device is operated in a second operating mode for a subsequently incoming sheet that is to be deposited on a stack of the second stack delivery. The active surface is moved, for at least the entire duration of the existing form- or friction-fit operating contact, with a speed between the respect sheet and the active surface. That speed corresponds approximately, i.e. with a deviation of ±10%, to the conveying speed of the conveyor system.