The carotid artery lies medial to the internal jugular vein, and the vagus nerve is situated posteriorly between the two vessels. In the upper part, the carotid sheath also contains the glossopharyngeal nerve (IX), the accessory nerve (XI), and the hypoglossal nerve (XII), which pierce the fascia of the carotid sheath.he carotid sheath is an anatomical term for the fibrous connective tissue that surrounds the vascular compartment of the neck. It is part of the deep cervical fascia of the neck, below the superficial cervical fascia meaning the subcutaneous adipose tissue immediately beneath the skin.