An intraluminal vascular prosthesis system for implantation in the region of the aortic arch of a patient, comprising: - a hollow-cylindrical main vessel prosthesis, which has a lumen routed through the main vessel prosthesis, a first lumen end, a second lumen end, a hollow-cylindrical stent frame, optionally with a prosthesis material secured thereon, a length L1 and a diameter D1, wherein the hollow-cylindrical main vessel prosthesis is configured and dimensioned for implantation in the region of the aortic arch and the descending aorta of the patient, and wherein the main vessel prosthesis has - at least one hollow-cylindrical anchoring vessel prosthesis, which has a lumen routed through the anchoring vessel prosthesis, a first lumen end, a second lumen end, a hollow-cylindrical stent frame, optionally with a prosthesis material secured thereon, a length L2 and a diameter D2, wherein the anchoring vessel prosthesis is securely attached within the lumen of 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 L1 of the main vessel prosthesis, wherein the vascular prosthesis system moreover comprises - at least one hollow-cylindrical side vessel prosthesis, with a lumen routed through the side vessel prosthesis, wherein the side vessel prosthesis has a first lumen end, a second lumen end, a hollow-cylindrical stent frame, optionally with a prosthesis material secured thereon, a length L3 and a diameter D3, and wherein the hollow-cylindrical side vessel prosthesis for implantation is designed and dimensioned to bridge the outlet of the subclavian artery and/or the carotid artery of the patient, in such a way that the side vessel prosthesis can be positioned with its first lumen end in the subclavian artery and/or the carotid artery, and, in order to securely anchor the side vessel prosthesis, its second lumen end can be inserted at least partially into and fixed in the lumen of the anchoring vessel prosthesis via the first lumen end of the anchoring vessel prosthesis, and wherein the second lumen end of the side vessel prosthesis is insertable, via the first lumen end of the main vessel prosthesis, into the first lumen end of the anchoring vessel prosthesis and at least partially into the lumen thereof. - a hollow-cylindrical main vessel prosthesis, which has a lumen routed through the main vessel prosthesis, a first lumen end, a second lumen end, a hollow-cylindrical stent frame, optionally with a prosthesis material secured thereon, a length L1 and a diameter D1, wherein the hollow-cylindrical main vessel prosthesis is configured and dimensioned for implantation in the region of the aortic arch and the descending aorta of the patient, and wherein the main vessel prosthesis has - at least one hollow-cylindrical anchoring vessel prosthesis, which has a lumen routed through the anchoring vessel prosthesis, a first lumen end, a second lumen end, a hollow-cylindrical stent frame, optionally with a prosthesis material secured thereon, a length L2 and a diameter D2, wherein the anchoring vessel prosthesis is securely attached within the lumen of 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 L1 of the main vessel prosthesis, wherein the vascular prosthesis system moreover comprises - at least one hollow-cylindrical side vessel prosthesis, with a lumen routed through the side vessel prosthesis, wherein the side vessel prosthesis has a first lumen end, a second lumen end, a hollow-cylindrical stent frame, optionally with a prosthesis material secured thereon, a length L3 and a diameter D3, and wherein the hollow-cylindrical side vessel prosthesis for implantation is designed and dimensioned to bridge the outlet of the subclavian artery and/or the carotid artery of the patient, in such a way that the side vessel prosthesis can be positioned with its first lumen end in the subclavian artery and/or the carotid artery, and, in order to securely anchor the side vessel prosthesis, its second lumen end can be inserted at least partially into and fixed in the lumen of the anchoring vessel prosthesis via the first lumen end of the anchoring vessel prosthesis, and wherein the second lumen end of the side vessel prosthesis is insertable, via the first lumen end of the main vessel prosthesis, into the first lumen end of the anchoring vessel prosthesis and at least partially into the lumen thereof.