Device for condensing sliver of fibres in spinning machines that comprises, - a tubular element which may be positioned at the outlet of a final pair of rollers of a spinning machine drawing unit which may be ∘ positioned parallel to the axis of said rollers, and ∘ connected to a source of vacuum, - the tubular element is provided with multiple transverse grooves for various drawing units of the spinning machine, and - bands which run on the tubular element, - each band is provided with small perforations and in turn may receive, on its surface remote from said tubular element, the sliver leaving the drafting unit and performing the transverse condensing of said sliver as it adapts to the empty grooves through the perforated band, - the tubular element having a gently curved structure in the adaption region of the perforated band, wherein - the device further comprises ∘ a drive cylinder inside the perforated bands and ∘ an upper roller ▪ the drive cylinder receives said tangential upper roller ▪ the upper roller has a resilient characteristic, characterized in that - said bands are mounted in contact ∘ with the part of the tubular suction element that has the grooves, ∘ with a peripheral region of the drive cylinder, and ∘ with a bar provided with small longitudinal recesses for tensioning and guiding said bands, - the drive cylinder is actuated by a longitudinal transmission shaft which may be positioned along said various drawing units of the spinning machine, - said drive cylinder has a toothed pinion which meshes with a transmission wheel of said transmission shaft, - said longitudinal transmission shaft is actuated by a servomotor. - a tubular element which may be positioned at the outlet of a final pair of rollers of a spinning machine drawing unit which may be ∘ positioned parallel to the axis of said rollers, and ∘ connected to a source of vacuum, ∘ positioned parallel to the axis of said rollers, and ∘ connected to a source of vacuum, - the tubular element is provided with multiple transverse grooves for various drawing units of the spinning machine, and - bands which run on the tubular element, - each band is provided with small perforations and in turn may receive, on its surface remote from said tubular element, the sliver leaving the drafting unit and performing the transverse condensing of said sliver as it adapts to the empty grooves through the perforated band, - the tubular element having a gently curved structure in the adaption region of the perforated band, wherein - the device further comprises ∘ a drive cylinder inside the perforated bands and ∘ an upper roller ▪ the drive cylinder receives said tangential upper roller ▪ the upper roller has a resilient characteristic, characterized in that ∘ a drive cylinder inside the perforated bands and ∘ an upper roller ▪ the drive cylinder receives said tangential upper roller ▪ the upper roller has a resilient characteristic, characterized in that ▪ the drive cylinder receives said tangential upper roller ▪ the upper roller has a resilient characteristic, characterized in that - said bands are mounted in contact ∘ with the part of the tubular suction element that has the grooves, ∘ with a peripheral region of the drive cylinder, and ∘ with a bar provided with small longitudinal recesses for tensioning and guiding said bands, ∘ with the part of the tubular suction element that has the grooves, ∘ with a peripheral region of the drive cylinder, and ∘ with a bar provided with small longitudinal recesses for tensioning and guiding said bands, - the drive cylinder is actuated by a longitudinal transmission shaft which may be positioned along said various drawing units of the spinning machine, - said drive cylinder has a toothed pinion which meshes with a transmission wheel of said transmission shaft, - said longitudinal transmission shaft is actuated by a servomotor.