The right-sided aorta is a rare congenital abnormality of the cardiovascular system encountered in 0.05-0.1% of cases during roentgenological examinations and in 0.04-0.1% of cases of autopsy series. Given utterly low prevalence of this pathology, we considered it wise to present herein our own case report dealing with hybrid surgical management of a patient suffering from an aneurysm of both the arch and descending portion of the right-sided aorta combined with type B dissection thereof and decompensated tracheal stenosis. The first stage of the operation consisted in prosthetic repair of the distal third of the arch and the descending portion of the aorta with the "Vascutek" stent graft 20 mm with type 1 haemodynamical correction (i. e., re-establishing the blood flow into the true channel in the zone of the distal anastomosis) in the conditions of extracorporeal circulation (EC) and bihemispheric antegrade cerebral perfusion ACP, followed by replantation of the left subclavian artery ostium into the left common carotid artery. An aneurysmal growth rate of more than 1 cm a year was considered an absolute indication for the second stage of correction of the aortic pathology concerned. The second stage included stenting of the thoracic portion of the aorta. The TF262C150X Valiant thoracic stent graft was implanted into the area of the distal anastomosis with a conduit, followed by positioning the TF 323C150X Valiant thoracic system inserted into the distal end of the first stent. The use of hybrid techniques (a combination of open and endovascular interventions) predetermined the success of surgical management of the patient presenting with dissection of the right-sided aorta.