Voting has ended in the Palestinian election to choose a successor to the late leader Yasser Arafat.
Mahmoud Abbas, seen as a moderate, is the frontrunner
Early indications suggest former prime minister Mahmoud Abbas is well ahead of his six rival candidates.
Analysts say he needs a wide margin of victory - and high turnout - to push his agenda of peace talks and an end to the armed Palestinian uprising.
Polling closed at 1900 GMT, two hours later than scheduled after voting difficulties forced an extension.
One exit poll by the Palestinian Centre for Policy and Survey Research gave Mr Abbas 66% of the vote and his closest challenger, Mustafa Barghouti, 19.7%.
Candidates: Mahmoud Abbas (Fatah), Mustafa Barghouti, Tayser Khalid (DFLP), Bassam al-Salhi (leftist), Sayyed Baraka, Abdul Karim Shubayr, and Abdul Halim Ashqar
Hamas is boycotting vote
Voting at 3,000 polling stations between 0500 and 1700 GMT
1.8 million eligible voters
More than 500 international observers and thousands of local monitors
Official result on 10 January
A second by An Najah University gave Mr Abbas 69.5% and Mr Barghouti 24.5%.
However, a late surge in voting means it may be some time before official figures are known.
Although a final result is not expected until Monday, correspondents report that supporters of Mr Abbas are already celebrating - waving flags and carrying posters of the man they are sure will be the new president.
But the extent of his margin as well as the level of voter turnout are seen as key if Mr Abbas is to claim a clear mandate.
About 1.1m Palestinians had registered to vote in their first presidential election since 1996.
Voting was reported brisk but there were problems with registration, heavy turnout and the turning away of hundreds of voters from a big Israeli-run polling station in East Jerusalem.
Some chaotic scenes were reported there.
Voters complained that Israeli officials were not allowing them to vote even though the Palestinian central election commission had properly registered them.
One election monitor said he thought up to 500 voters had been turned away.
Under special voting arrangements for East Jerusalem - which Israel has annexed and sees as its exclusive domain, while international law decrees it to be occupied territory - Palestinians are allowed to vote in Israeli post offices.
Only minor problems were reported elsewhere, although in a polling station in Ramallah in the West Bank, five Palestinian gunmen fired into the air in frustration that some names had been left off lists.
They were persuaded to leave the station.
The BBC News website's Martin Asser says the extension had put pressure on polling station staff who were already complaining of fatigue after working non-stop for 12 hours.
Earlier, casting his vote at the Ramallah compound where Arafat is buried, Mr Abbas - also known as Abu Mazen - said the vote was taking place in a "marvellous" fashion.
"It is an illustration of how the Palestinian people aspire to democracy," he said.
Palestinian militant group Hamas had called for a boycott of the vote.
However, on Sunday a Hamas spokesman, Sami Abu Zuhri, said: "We will deal with the elected president despite our boycott."
Israel said it had done what it could to ease travel restrictions for the vote, including removing a number of temporary roadblocks. But some Palestinians said they had not gone far enough.
An Israeli military source said: "If there were any delays they were because of intelligence alerts. We told the Palestinians we reserved the right to act on alerts."
The former French Prime Minister Michel Rocard, the head of the European Union's monitoring mission, said he had seen no serious problems at checkpoints.
The death of Arafat in a Paris hospital in November has raised hopes for new peace talks between the Palestinians and Israelis.
Israeli Prime Minister Ariel Sharon had refused to do business with Arafat.
As Palestinians went to the polls, Israel's Labour Party leader Shimon Peres, who is entering a new coalition government with Mr Sharon, told the BBC he thought "very highly" of Mr Abbas.