American Samoa's chief immigration officer Ufuti Fa'afetai Ieremia estimates that there are now some 800-plus overstayers in the territory.
Ufuti made the comments at a Senate committee hearing on a bill that would fine sponsors of a foreigner staying beyond the permitted time.
He has also testified that the majority of overstayers are from neighbouring Samoa.
Ufuti says in December every year about 500 of them depart the territory and thereby reduce the number of overstayers.
He points out daily flights from Samoa bring in more travellers that can become overstayers as they enter on a 14-day permit or a 30-day visitor's permit.