A stent graft defining a main lumen bounded by a wall of graft material is disclosed. The stent graft has a valve portion between proximal and distal portions. The valve portion is formed by a wall portion having a part-circumferential double layer portion comprising an inner underlap portion and an outer overlap portion, the double layer portion forming a passageway parallel to the main lumen. The passageway has an entrance mouth and an exit mouth. The passageway has an open condition where the underlap and overlap portions are spaced apart to form a vent lumen. The wall portion is broken by a narrow cut. The cut is openable by relative radial movement between its edges. This allows re-perfusion of an aneurism and perfusion of blood from within the lumen out towards blood vessels such as intercostals and can assist in minimizing the chance of paraplegia.