An endovascular graft prosthesis for arrangement at or in the vicinity of a bifurcation in the arterial system of a patient, e.g. for the purpose of repairing an aneurysm or the aortic bifurcation comprises a substantially tubular main body for location in the principal upstream arteria above the bifurcation such as th aorta and substantially tubular legs joining said main body in a bifurcation and extending into each of two branch arteries such as the iliac arteries. The main body (8) is substantially bag-shaped with an open proximal upstream end and a distal downstream bottom region in which two outlet openings (9, 10) are provided and is attachable to the inner side of the principal arteria (2) by means of an expandable stent device (11). The legs are made as separate expandable leg stent devices (15, 16) which may be introduced in a collapsed condition through the branch arteries and into the outlet openings (9,10) of the main body by means of guide wires (13,14) to engage against the rim of the corresponding outlet opening to provide a leakage-free bifurcated graft prosthesis.