A mounting head (T) for mounting a pump or a valve on a neck (22) of a reservoir (2), the mounting head (T) having a mounting member (3) for imparting an axial mounting movement from an axial arrangement placed on the neck (22). The mounting member (3) has a centering mechanism (35, 36, 4) bringing the dispenser member (1) into an axial arrangement on the neck (22) if offset. The mounting head (3) has mounting tabs (31) movable axially so as to bring the dispenser member (1) from the axial arrangement towards the final position, and movable radially inwards so as to return the dispenser member (1) into an axial arrangement. An outer clamping collar (4) simultaneously moves the mounting tabs (31) radially inwards from a spaced-apart rest position.