An apparatus for forming a stream of overlapping sheets or stacks of sheets, includes a first transport device to deliver overlap-free sheets or stacks of sheets at a speed v1 along a plane of transport EV. A second transport device carries away the sheets or stacks of sheets at a speed v2 along a plane of transport EH. A decelerating device is arranged to receive the sheets or stacks of sheets at the speed v1 from the first transport device, decelerate the sheets or stacks of sheets to the speed v2 and deliver the decelerated sheets or stacks of sheets to the second transport device to form the stream of overlapping sheets or stacks of sheets. The decelerating device comprises a suction roller unit actuated independently of the transport devices. The suction roller unit comprises a stationary element and an unevenly driven movable element.