When blankets (02) are mounted or dismounted on cylinders (01), rollers are fitted to said cylinders to ensure that winding and unwinding occurs in a homogeneous manner. One requirement is that the adjustment pressure should be homogeneous at low control and operating costs. According to the invention, several rollers (03) which can move independently from each other can be fitted to the cylinder simultaneously with the aid of a single means of adjustment (04) in order to create said device for pressing blankets onto cylinders. In a particular embodiment, first and second rollers for mounting or dismounting the blanket can be actuated.