A transport device for sleeve-shaped covers for cylinders in printing units of a printing press includes a translation element and a number of carrier elements for sleeve-shaped covers. The carrier elements are received on the translation element. A movement of the translation element causes at least a group of carrier elements to be positioned in the vicinity of cylinders of the printing press such that sleeve-shaped covers received on the carrier elements of the group are transferable directly from the carrier elements to the cylinders or that sleeve-shaped covers received on the cylinders are transferable directly to the carrier elements of the group. In the method of changing sleeve-shaped covers, groups of carrier elements are positioned in front of the cylinders so that the sleeve-shaped covers are taken off the cylinders and transferred directly to carrier elements or are transferred and mounted from carrier elements directly to cylinders and are mounted thereon.