A connecting device (2) for use in the treatment of wounds has a conduit (10) which can be evacuated and a flat, extended vacuum-tight carrier (12) on which the conduit (10) is held in a vacuum-tight fashion, wherein the carrier (12) can be disposed onto a vacuum dressing (6) covering the wound. The conduit (10) communicates with the wound space through openings. An adhesion-promoting layer (24) is provided on the side (22) of the carrier (12) facing the wound and has a middle supporting layer (26), a first adhesive layer (28) held on the supporting layer (26) and facing the carrier (12) and a second adhesive layer (30) held on the supporting layer (26) and facing away from the carrier (12). The adhesion-promoting layer does not block an opening (18) in the carrier (12).