An endoluminal self-expanding prosthesis for placement in a blood vessel, duct or lumen, to hold it open. The prosthesis includes a stent with a graft extending within the stent. The stent is an elongated self-expanding stent with an open tubular wall structure. The graft is an elongated compressible generally tubular graft. One end of the graft is secured to the inside of the stent and the graft extends therethrough. The stent is deployed allowing the free flow of blood through the open-celled structure, and the graft is freely deployed secondarily within the stent by the blood flowing therethrough. The present invention is not subject to significant distal migration during delivery and placement of the prosthesis.