Abstract: An unstacking apparatus comprises one or more sheet-entraining drums each having a peripheral depression, lying behind a rising forward edge, onto which the first sheet of a confronting stack is pulled by suction cups during every drum revolution. A counterpressure roller osscillatable about the drum axis is then swung from a position downstream of the depression past its forward edge, against the sense of rotation of the drum, to engage the pulled-off sheet and deliver it to a conveyor. Each counterpressure roller is spring biased toward the associated drum but is prevented by a stop from reaching the bottom of the depression in the absence of an entrained sheet. A sensor on the drum shaft or on the roller shaft emits an alarm signal whenever the distance between these shafts deviates from a predetermined range limit.