Abstract: For use in a web-handling apparatus, a cylinder module accumulates and de-accumulates web in a controlled manner. A frame supports first and second parallel main cylinders. The first cylinder rotates continuously, while the second cylinder operates in a non-uniform manner. A third main cylinder remains parallel with the first and second axes while moving perpendicular to those axes. The web passes around the first cylinder through the first nip, thence to and around the periphery of the third cylinder, thence to and partially around the periphery of the second cylinder and through the second nip. The web spans from the third cylinder are substantially parallel. An endless belt associated with each end of the third cylinder ensures that the third cylinder occupies an axis location and a rotational position which substantially control the web stress as the web passes through the cylinders.