A drainage tube device for removing fluids by suction from a human or animal body comprises a coupling unit with first and second coupling parts that can be connected to each other in a leaktight manner, a first valve that is arranged in the first coupling part, and a drainage tube with an end that is directed towards the patient and is held in the second coupling part. The drainage tube has a multi-lumen design with a drainage conduit and at least one auxiliary conduit. This drainage conduit and at least one of said auxiliary conduits are in fluidic communication with each other at their end directed towards the patient and arranged inside the second coupling part. The drainage tube device further comprises a second valve, which is arranged in the second coupling part and which opens and closes the drainage conduit. The drainage tube device and the coupling unit according to the invention are of simple construction but nonetheless permit many functions. In particular, they prevent dripping when the connection is released, and they allow pressure to be measured near the patient.