 The hypoglossal nerve crosses both the internal and external carotids, curving around the origin of the occipital artery.Within the sheath, between the artery and vein, and behind both, is the vagus nerve; behind the sheath, the sympathetic trunk.On the lateral side of the vessels, the accessory nerve runs for a short distance before it pierces the Sternocleidomastoideus; and on the medial side of the external carotid, just below the hyoid bone, the internal branch of the superior laryngeal nerve may be seen; and, still more inferiorly, the external branch of the same nerve.