An arteriovenous graft system is described. The arteriovenous graft system includes an arteriovenous graft that is well suited for use during hemodialysis. In order to minimize or prevent arterial steal, at least one valve device is positioned at the arterial end of the arteriovenous graft. In one embodiment, for instance, the arteriovenous graft system includes a first valve device positioned at the arterial end and a second valve device positioned at the venous end. In one embodiment, the valve devices may include an inflatable balloon that, when inflated, constricts and closes off the arteriovenous graft. If desired, a single actuator can be used to open and close both valve devices.