Abstract: An endoluminal prosthesis is provided for use in the treatment of a dilation in a body vessel. This dilation might be an abdominal aortic aneurysm or a dilation in a blood vessel wall following a balloon angioplasty procedure. The prosthesis comprises a radially expandable tubular member and a covering provided on the outer surface of the tubular member. The covering comprises first and second layers of material. The first layer comprises an agent that promotes swelling of the covering on exposure of the covering to contact with body fluid, such as blood. The second layer comprises space-filling material. When the prosthesis is delivered into the body vessel the tubular member can automatically expand or be expanded radially. The covering will also swell on the tubular member. This expansion and swelling forces the exterior of the swollen covering into intimate sealing contact with the surrounding inner wall of the vessel.