The first-round vote on April 9 brought complaints of widespread irregularities, stoking concerns of instability in the poor nation still struggling to heal divisions after its bloody separation from Indonesian rule.
Counting from this second round will initially be conducted at local polling stations before the results are then collated by the National Election Commission in the capital, Dili.
Share of 1st round vote: 22%
The 57-year-old Nobel Peace Prize winner became prime minister when the government fell last year amid widespread violence. Was country's first foreign minister. Close to outgoing President Xanana Gusmao. Has pledged to continue East Timor's co-operation with the UN.
FRANCISCO 'LU-OLO' GUTERRES
Share of 1st round vote: 28%
The president of Fretilin, a left-leaning political party formed out of armed resistance to Indonesian rule. Now aged 52, he spent the years under Indonesian occupation fighting in East Timor's hills and jungles. One of eight children, he has sought to portray himself as a man of the people.
Ramos-Horta and Guterres won the most votes out of eight candidates in the first round, but neither won a clear majority, forcing a run-off.
The vote is seen as critical to maintaining peace a year after the troubled nation was pushed to the brink of civil war.
Ramos-Horta, 57, a Nobel peace prize winner who spearheaded an overseas campaign for East Timor's independence, appears to have the edge after five of the first-round losers urged their supporters to vote for him.
Guterres, however, is seen as a strong challenger.
He is backed up by Fretilin, the well-organised political party of the nation's former armed resistance to Indonesian rule.
He has fought a hard campaign, portraying himself as a man of the people in contrast to Ramos-Horta's image as a foreign-educated intellectual.
Turning out to cast his cote on Wednesday morning, Ramos-Horta said he was "totally relaxed" and ready to accept the decision of voters.
"If I win the election, I win a ... huge responsibility," he said. "But if I lose, I win my freedom to do whatever I want, to be a writer, to be an academic, to be a tourist, to travel."
He said he would honour the results even if they were not 100 per cent clean.
|Tight security was in place at polling |
stations amid fears of violence [AFP]
Guterres also pledged to accept the results of the election.
"I will become the Timorese president to serve the people, resolve the crisis and establish peace and democracy," he said after voting.
"I want to win with dignity, but if I lose, I will also accept that with dignity."
More than 522,000 people were registered to vote to replace Xanana Gusmao, the former resistance leader who became East Timor's first president.
On Tuesday Gusmao, who will run for the post of prime minister in parliamentary elections scheduled for June, called on voters to focus on the national interest.
The post of prime minister carries more power than the presidency, which is a largely ceremonial role.
Last May the country descended into bloodshed after Mari Alkatiri, the then-prime minister, sacked 600 mutinous troops from the west of the country.
At least 37 people were killed and some 155,000 fled their homes before the government collapsed.
Foreign troops had to be brought in to restore order but 30,000 people remain in camps across Dili, too afraid to go home.
East Timor is one of the poorest nations in Asia, with average per capita income of less than $1 a day, unemployment estimated at 50 per cent and about 60 per cent of its children suffering from malnutrition.