Abstract: In an apparatus for cutting, decelerating and overlapping sheets of paper, comprising means for feeding a paper web at predetermined speed, means for cutting said web into sheets, suction means for decelerating the sheets, means for adjusting the amount of suction in relation to the feeding speed, and means for stacking the decelerated sheets, the improvement wherein said suction means includes an ejector roller provided with recesses and located directly in front of the stacking means, at least one suction strip provided in a recess of the ejector roller and extending approximately to the apex of the ejector roller, and at least one nozzle provided in the area of the ejector roller directing air toward the stacker so as to form an air cushion between the sheet being stacked and the sheet which had just previously been stacked.