A device for drying a running web, particularly a drying section of a paper manufacturing or processing machine. In the drying section, at least one drying cylinder, which can be heated and comes into contact with the web, is provided in each of successive cylinder groups. Each cylinder group has its own drive. At least one two-felt cylinder group is provided in which, the web runs in serpentine fashion alternately over upper cylinders, felted above, and lower cylinders, felted below. At least one additional cylinder group, provided with its own additional drive, is provided adjacent the two-felt cylinder group. Between the two-felt cylinder group and the additional cylinder group there is a free web path at which a tail-cutter is arranged.