People have been queuing in the Vanuatu capital Port Vila to cast their vote for a replacement for the late Edward Natapei.
One of the six seats in the capital constituency has been vacant since Mr Natapei's death in July.
He was the leader of the opposition at the time.
The 37 324 have a choice of six candidates including two women.
The 12 polling stations include a booth in the New Caledonian capital Noumea which is home to many ni-Vanuatu.
Mr Natapei's son Kenneth Natapei is also contesting the election.
One of the women candidates is standing as an independent and the other is standing for the People's Progressive Party of Prime Minister Sato Kilman.
The polling stations close at 4.30pm and unofficial results are expected tonight.