A xenon-based anesthetic gas to be used, via inhalation, to maintain or preserve cerebral perfusion during an endarterectomy involving the clamping of the carotid artery in a mammal under general anesthesia. The xenon is preferably used in combination with at least one injectable anesthetic morphine agent such as remifentanil, sulfentanil, fentanyl, and alfentanil. Advantageously, the xenon is mixed with an oxygen-containing gas and administered to the patient after the patient has been anesthetized, put to sleep, and intubated. The use of xenon makes it possible to achieve a reduction in the pressure gradient during the clamping of the internal carotid artery relative to the usual anesthetic agents, and to achieve stable hemodynamics.
