Apparatus for assembling sheets into a stack, the apparatus comprising a stacking station having two laterally spaced guide elements (25A, 25B) defining first and second guide surfaces fixed relatively to one another. First and second transport systems (2, 3; 9, 11, 12) define respective first and second paths, the first transport system being adapted to transport sheets along the first path to the stacking station (24) and the second transport system being adapted to transport sheets in both directions along the second path between positions upstream and downstream of the stacking station (24). The guide elements (25A, 25B) are movable between first and second positions (25', 25). In the first position sheets fed along the first and second paths from positions upstream of the stacking station (24) are guided along respective ones of the first and second guide surfaces past the guide means to a position downstream of the stacking station in the second path. In the second position the guide elements (25A, 258) enable sheets in the second path to be moved between positions upstream and downstream of the stacking station (24) along the second path guided by the second surface and prevent sheets from passing into the first path. A microprocessor (31) controls operation of the first and second transport systems and the position of the guide elements (25A, 25B) such that when the guide elements are in the first position, the speeds of the first and second transport systems are controlled whereby sheets fed along the first and second paths from upstream of the stacking station (24) are assembled together in a stack in the second path downstream of the stacking station.