A stack (7) piled from a feed conveyor (3) can be transferred with stack definitions (15, 16) which can be lowered and optionally shifted in opposite directions to the left or right onto an exit conveyor (4 or 5), whilst the stack plies (6) continuing to be fed are intercepted by an auxiliary means (40, 50) and lowered onto the stack support (8) following return of the stack definition (15, 16) into the stacking position, as a result of which very simple and gentle exit transport of the stacks (7) materializes at high working speed.