Abstract: A cannula or catheter assembly has a cannula or catheter tube in a socket with a straight passageway. In order to equip such an assembly with a cheap and safe closure device which is easy to maneuvre without causing any movements injurious to the assembly, a connecting housing is fixedly or releasably connected to the socket and has a straight through-channel which is connected to the passageway of the socket and accommodates a hose section which seals against the channel wall and, to permit closing the through-channel, can be compressed at a location between its ends by means of at least one pressure body disposed in an opening in the wall of the through-channel and operable by means of a slide member movable in the axial direction of the through-channel on the outer side of the connecting housing.