A web-fed rotary printing press, which is used for printing a web has at least four printing points or locations that are allocated to the web in an imprinting mode of the press. At least one of each two printing points or locations can be alternatively engaged with the web. These two printing points apply the same ink to the same side of the web. These two printing points or locations are situated in two different printing units. In each of the operating modes of the press, at least one of the printing points or locations in each of the units is in a print-on position.