Device for treating wounds with reduced pressure. The device comprises a sealing film, which is placed sealingly around the wound to cover the latter, an underpressure source, as well as a tube, which connects a space over the wound and beneath the sealing film to the underpressure source. The interior of the tube comprises a longitudinal first strand made of a hydrophobic material, as well as a second strand, made of an open-pored hydrophilic material, extending longitudinally over at least a part of the length of the tube. The said material strands are enclosed in a tube casing made of a flexible material.