The invention relates to a stack storage device for a printing device. The sheets that are supplied to an output unit of a printing device are stacked by the stack storage device to form a stack (30) of a predetermined height. Several of these stacked stacks of sheets are temporarily stored on a conveyor device (22) of the inventive stack storage device. This is a simple means of obtaining a considerable sheet capacity while keeping the stack size of the individual stacks (30) of sheets relatively small so that they are easy to handle. A considerable advantage of the invention is that it can easily be retrofitted or linked to known printing devices.