The gag reflex is primarily mediated by the afferent fibers of the glossopharyngeal nerve (CN IX), which detect sensory stimuli in the oropharynx. The efferent response is carried out by the vagus nerve (CN X), but the trigeminal nerve (CN V) also contributes sensory input from the anterior tongue and oral mucosa, triggering the reflex. Therefore, both glossopharyngeal and trigeminal nerves are implicated in initiating a strong gag reflex. Understanding this is crucial during oropharyngeal procedures to anticipate patient response and avoid complications such as aspiration or airway obstruction.

Reference: Gray's Anatomy, Standring S, 42nd Edition.