An endoluminal prosthesis is provided that includes a tubular graft and an expandable annular support structure for use in a body lumen through which body fluids flow. The annular support structure is coupled to the tubular graft where it is to be sealingly engaged with the inner wall of a body lumen so that the graft and support structure, in combination, provide an improved seal. An embodiment according to the invention provides an annular structure with longitudinally staggered apices providing multiple levels of contact with the inner body lumen wall to provide a seal at multiple levels along the length of the prosthesis. One embodiment relates to tubular grafts for endoluminal placement within blood vessels for the treatment of abdominal and other aneurysms.