A printing press is comprised of at least one dry offset printing unit. At least two different webs can be fed through the dry offset printing unit. In a first production mode “C” of the printing press, a first web is fed through the dry offset printing unit without a subsequent drying process. In a second production mode “H” of the printing press, a second web is fed through the dry offset printing unit and through an active dryer. In both the first and second production modes “C”, “H”, an inking unit of the printing unit is filled with the same ink.