In an apparatus for the fibre-sorting or fibre-selection of a fibre bundle comprising textile fibres, especially for combing, which is supplied to a fibre-sorting device, especially a combing device, having clamping devices which clamp the fibre bundle at a distance from its free end, which is combed to remove non-clamped constituents, the clamping devices each comprise two clamping jaws. To increase productivity and to enable an improved combed sliver to be obtained, downstream of the supply device there are arranged at least two rotatably mounted rollers rotating rapidly without interruption, the clamping devices being spaced apart in the region of the periphery of the rollers, and each clamping device comprising at least one nipper part which is at least partially resilient. The clamping jaws may have a high coefficient of friction in the region of their clamping surfaces.