Abstract: A process and device for compacting stacks of cutouts in a packaging machine wherein the stacks arranged in an orderly manner are removed by a grip element supported by a head of a removal and transfer unit. The stack is transferred to a compacting station fixedly mounted in a position above a feeding station of the packaging machine. and is inserted in the compacting station which is equipped with an abutment element having an inlet shaped complementarily to one end of the cutouts. Pusher elements which are rigidly associated to the head and frontally define a profile being shaped complementarily with respect to the end of the cutouts opposite to the one inserted in the compacting station, act on the stack upon advancement of the head for inserting the stack in the inlet of the abutment element, thereby compacting the stack.