The oculomotor nerve is one of the cranial nerves. As it name suggests, it connects to most of the muscles that control the movement of the eyes, pupil and eyelids.

The nerve can be damaged by trauma, demyelinating diseases, increased intracranial pressure or diseases that damage microvessels, such as diabetes mellitus.

Several simple clinical tests test for the function of the oculomotor and related nerves. For example, a person with a normal oculomotor nerve can easily follow the doctor's moving finger tracing out an "H" pattern without having to move their head. Damage to the nerve also manifests as a constant gaze downward. Damage should also be suspected if the pupil reflex is not normal.

Oculomotor nerve at Wikipedia