The present disclosure relates an apparatus for controlling the lateral offset of webs of material. The apparatus can include a support structure for supporting a roll and a mechanism for lifting the web of material off the roll. The support structure can include a fixed portion and at least one movable portion. The roll is preferably journaled to first mountings, the first mountings being attached to the movable portion of the support structure, so that the roll can be moved together with the first mountings. A potential advantage of this design is that the journal bearing of the roll on a respective shaft can be configured more easily and given smaller dimensions. According to a further aspect of the disclosure, the lifting mechanism can include at least two single rollers, rotatably journaled to two lateral supports. Such single rollers are advantageously arranged along a circular-arc plane. The web of material can thus be deflected with as large a radius as possible. This can reduce undesirable back-sway of the sagging portion of the web of material as a result of the intermittent operation. The end portions of the circular-arc plane can also extend tangentially to the provided direction of travel of the web of material, thereby potentially resulting in crease-free deflection of the web of material.