Why do my nephew's eyes constantly move around?

Nystagmus. He likely has an ocular condition that is termed nystagmus. This is an involuntary movement of the eyes back and forth either horizontally, vertically or oscillatory. Nystagmus can be congenital or acquired. Interestingly, congenital nystagmus does not result in the person seeing the world as "jumping around." acquired nystagmus is usually a sign of a neurologic condition that requires a work-up.