Apparatus for sheet singling and alignment on a top side of a sheet pile of a rotary printing press includes a suction device extending transversely to sheet transport direction in the vicinity of the leading edge of the sheet pile, the suction device being intermittently activatable with suction air, a scanning device for controlling a lifting motion of the sheet pile, the scanning device extending across the entire width of the pile and having a member movable towards and away from the top side of the pile for scanning the height thereof, swivelable levers adjacent the pile-height scanning member, an element for laterally aligning single sheets of the sheet pile axially displaceably mounted on the swivelable levers, and a device for directing an air stream onto the leading edge of the sheet pile so as to lift off a leading-edge region of the respective single sheets from the pile.