The device (6) has two end sections (7,8) with anchor elements (18), which engage into holders (5) on the vehicle. A winding roller (23) is turnable in, and axially moveable relative to, the end sections. A roll-up cover (11) is fastened to the roller. A drive unit (24) supported on the end sections rotates the roller to roll-up the cover. Springs between roller ends and end sections tension the sections axially away from the roller. An actuator unit with manual actuator connects the end sections to move them towards each other.
