A stent graft defining a main lumen (11) bounded by a wall (12) of biocompatible graft material is disclosed. The stent graft has a valve portion (60) between proximal and distal ends. The valve portion (60) is formed by a wall portion (62) having a part-circumferential double layer portion comprising an inner underlap portion (64) and an outer overlap portion(66), the double layer portion forming a passageway parallel to the main lumen (11). The passageway has an entrance mouth (61) and an exit mouth (69), the exit mouth closer to a proximal end of the stent graft than the entrance mouth (61). The passageway has a closed condition where the underlap and overlap portions are in contact and an open condition where the underlap and overlap portions are spaced apart to form a vent lumen (40). The wall portion can be broken by a narrow cut or slot (70), the cut having a first edge (72) and a second edge (74). The cut is openable by relative radial movement of the first edge (72) away from the second edge (74). This allows re-perfusion of an aneurism and perfusion of blood from within the lumen out towards blood vessels such as intercostals and hence can assist in minimising the chance of paraplegia.
