Abstract: An apparatus for rolling strip having a periodically fluctuating strip thickness has a roll stand with a set of rollers defining a gap, an adjustment actuator for adjusting the gap of the set of rollers, unwinder for feeding the strip with an initial thickness to an intake side of the roller gap, winder for receiving the strip with a desired final thickness from an output side of the gap, respective upstream and roller assemblies each having an immersion roller provided upstream of the roll stand between the unwinder and the roll stand and downstream of the roll stand between the roll stand and the winder. The strip is guided around the immersion rollers. A controller sets positions of the immersion rollers while operating the rollers of the roll stand at a constant roller speed, for determining the roller gap in dependence on the setting of the rollers.