Excess liquid is removed from a fast-moving thread, in that the latter is deflected, so that the liquid is hurled off, the hurled off liquid is removed from the thread, in that the thread is passed through a closed chamber, where a vacuum is produced in order to facilitate liquid evaporation and in that the thread is led through a narrow gap, so that the layer directly surrounding the thread and travelling therewith is peeled off. The combination of these drying effects constitutes one process stage. Advantageously, this process stage is performed several times in direct succession, so that in the case of a thread-protecting, small deflection angle a good thread drying can be achieved. The process is performed by an apparatus comprising several chambers (K.1-3) connected in series in the thread movement direction, the thread being deflected at the inlet and/or outlet with respect to each chamber by a deflection element (U.1-4) and passes through a narrow gap (S.1-). The chamber walls (20.1-4), which carry the thread passage, are inclined away from the thread in the gravity direction. The hurled off liquid, under the influence of gravity flows through corresponding passages, which interconnect the chambers and passes into the final chamber in the thread movement direction and is sucked off from the latter.