An assembly having a stabiliser and an instrument to be positioned in or around a passage surrounded by body tissue, in particular vascular tissue. The stabiliser is provided with one or more suction mouths running in the shape of a loop, which suction mouths can be operationally connected to suction means in order to suck tightly to tissue close to and around said passage, which may still have to be made. The instrument has a head section for performing operations on vascular tissue. The stabiliser and the instrument are provided with, respectively, an instrument stop provided on the stabiliser and a stabiliser stop provided on the instrument, which, in the stop position when they are in contact with one another, unambiguously define the position of the head section with respect to the position of the loop shape. The instrument can be an applicator for positioning and fixing a fixing device in or around the passage, the head section being equipped for carrying and releasing the fixing device.
