The present invention relates to an intraluminal vessel prosthesis system for implantation in the region of the aortic arch of a patient, comprising a hollow cylindrical main vessel prosthesis, wherein the hollow cylindrical main vessel prosthesis is configured and dimensioned for implantation in the region of the artic arch and the descending aorta (Aorta descendens) of the patient and wherein the main vessel prosthesis, at least over part of the length L2 of the anchoring vessel prosthesis, and wherein the diameter D2 of the anchoring vessel prosthesis is at least 45% smaller than the diameter D1 of the main vessel prosthesis and wherein the length L2 of the anchoring vessel prosthesis is shorter than the length L2 of the main vessel prosthesis.
