The instrument has a hollow shaft (2), so that two channels are arranged in the shaft and are coupled on a proximal end with supply conduits. A proximal end of one of the channels positioned in the shaft and the distal end of the supply conduit coupled with the channel is arranged in a way that the channel and the corresponding supply conduit are coupled only with one another, with respect to the geometric structural design. A connecting adapter is secured to the medical instrument by a coupling mechanism (16) e.g. catch connection.
