Sekdah Somon and Buxoo Nabilah Bibi have been detained and face more than 300 charges over their alleged trafficking of dozens of Bangladeshi men.
A group of 101 migrants have been under state care in Port Vila since November and efforts are underway to repatriate them to Bangladesh.
The defendants' lawyer, Andrew Bal, filed to cease to act on their behalf last week.
The pair have told the Vanuatu High Court they are working to get a foreign counsel to represent them.
Without legal representation, a case hearing last Tuesday was postponed until tomorrow.