The tiny South Pacific territory of Tokelau is voting on whether to become one of the world's smallest self-governing states.
The 1,500 islanders are holding a referendum, which could reclaim Tokelau's sovereignty for the first time in 120 years.
Tokelau - made up of three coral atolls which have no airport, roads or capital - has been governed by New Zealand.
Four UN observers have made the 28-hour trip. Votes will be collected by ship.
Each island - Atafu, Nukunonu and Fakaofo - will vote on successive days. Tokelauans based in the Samoan capital Apia, some 300 miles (500km) south, voted on Saturday.
Results of the referendum are expected within five days.
Tokelau's three specks of land make up just 4.7 sq miles (12 sq km), lying halfway between Hawaii and New Zealand.
WORLD'S SMALLEST STATES
Vatican City, Europe: 0.44 sq-km (0.17 sq mile) residence of spiritual leadership of Roman Catholic church, pop. 900
Monaco, Europe: 1.95 sq-km (0.75 sq mile) playground for tourists and wealthy, pop. 32,000
Nauru, Asia-Pacific: 21 sq-km (8 sq miles) Pacific island and world's smallest republic, pop. 9,900
Tuvalu, Asia-Pacific: 26 sq-km (10 sq miles) group of nine islands in South Pacific, pop. 10,000
San Marino, Europe: 61.2 sq-km (23.6 sq miles) territory surrounded by Italy; world's second smallest republic, pop. 27,000
Seized by Britain in 1889, they were handed to New Zealand to administer in 1926.
With an annual income of just $2m, Tokelau could not exist without New Zealand aid, says the BBC's Greg Ward in Auckland.
The islands' 600 registered voters will decide whether Tokelau should remain a dependent territory or become self-governing, in free association with New Zealand.
New Zealand administrator for the territory, Neil Walter, said Tokelau had been in full control of its own affairs, with New Zealand support, for a number of years already.
"This act of self-determination would... simply formalise that position," he was quoted by the Associated Press as saying.
The referendum has been welcomed by New Zealand's Prime Minister Helen Clark who says aid from her country is guaranteed whatever the outcome.
But some Tokelauans "question whether this is the right time" to cut free from New Zealand, says Apia-based Falani Aukuso, head of Tokelau's government service.