The invention relates to devices for aligning sheets (1), which are overlapped with an offset and supplied to the device by a stream feeder and which can be transferred to a device (63) that is located downstream, after alignment of the front edge and one lateral edge of the sheets. At least pant of a sheet can be brought to rest on the periphery of an alignment cylinder (62), which is used to align the front edge of the sheet by means of front lay marks located on the periphery of said cylinder. At least one recess is provided on the periphery of the alignment cylinder, which, by the application of a negative pressure to said recess allows at least part of the sheet to be fixed by friction on the periphery of the alignment cylinder, in such a way that in the contact zone, drive forces from said cylinder can be transferred by friction to the sheet. A measuring device (64) determines the offset of a lateral edge of the sheet in relation to a predetermined set alignment. A transversal displacement device is used to align a lateral edge of the sheet in accordance with the measurement result of the measuring device. The acceleration and/or speed and/or angle of rotation of the drive motor for driving the rotation of the alignment cylinder can be controlled or adjusted according to predetermined laws of motion, in particular in accordance with the angle of rotation of the alignment cylinder.