Abstract: An apparatus for clamping an individual thread out of a plurality of threads, which are guided in side-by-side relationship, includes a transport unit with a drivable transport shaft and a rotatable contact pressure shaft. A thread is guided between the shafts. A clamping unit with an abutment and a clamping pin acting thereagainst is used for clamping a respective thread. Between the clamping pin and one of the functional parts of the transport unit, there is an operative connection. Increasing the clamping of a thread in the clamping unit causes an increasing release of the thread in the transport unit and vice-versa. The operative connection can adopt a central position in which the thread is loose both in the transport unit and in the clamping unit.