A composite stent graft has a balloon expandable stent portion (3), a tubular graft material portion (1) inside or outside of the balloon expandable stent portion and self expanding stents (5) associated with the tubular graft material portion. Part (7) of the balloon expandable stent portion can extend beyond the proximal end (9) of the tubular graft material portion. The tubular graft material can be polytetrafluoroethylene, Dacron, Thoralon™, polyamide, small intestine submucosa, collagenous extracellular matrix material, or any other suitable biocompatible material. A method of deploying which includes flaring a part (7) of the balloon expandable stent portion is also discussed.
