People have been lining up at polling stations throughout the West Bank and Gaza to vote for a successor to Yasser Arafat as president of the Palestinian Authority.
By Martin Asser
BBC News, Ramallah
For Ramallah, high up in the hills around Jerusalem, it was a cold, crisp start to the day, perhaps putting some voters off until there was a bit of warmth in the winter sunshine.
Voting at most polling stations has been smooth
Nevertheless, at the Friends Boys School voting centre they had already had 10% of their 2,000 registered voters through the doors by about 0900, two hours after polls opened.
But mostly there were many more international observers and, in particular, journalists at the station than voters.
This was because this is where Mustafa Barghouti, the main challenger to frontrunner Mahmoud Abbas according to the polls, was set to vote.
A huge media scrum engulfed the candidate when he arrived, brandishing a copy of al-Quds newspaper that - much to his chagrin - was carrying a full-page advert in support of Mr Abbas, also known as Abu Mazen.
The advert appeared to directly contravene the election law that said campaigning activity must end at midnight on the Friday before polling.
As the candidate raised his complaints to the world's television cameras, a member of his team was also going around showing how she had been able to scrub the supposedly indelible ink from her thumb - proving that unscrupulous people may be able to vote more than once.
Barghouti's challenge is considered vital to the credibility of the election
Apart from that, the Barghouti voting excursion was marred by an attempt by some opponents of his to display handwritten placards inside the school walls accusing him of corruption and saying doctors should not become politicians.
The candidate himself was unaware of this breach of election protocol, but some of his minders quickly dealt with it by seizing the placards and tearing them up.
"I was only trying to express my opinion," one young man who had been involved in the anti-Barghouti protest remonstrated with the voting centre officials.
"They didn't have to rip up the placards up!"
For the most part voting has gone very smoothly, with people waiting patiently to present their registration receipts and ID cards so they can enter the schools that serve as polling stations.
The receipts tell them which section to vote in, from usually four or five classrooms, where their names and details are checked.
Problems have arisen where people who have registered find that their names are not on the polling centre list and they are not allowed to vote.
Problems have arisen where voters' names are not on polling centre list
I and other witnesses saw this occur in a small number of cases - perhaps as a result of carelessness on the part of election officials - at several polling stations in Ramallah and neighbouring Bireh.
In each case I witnessed, the voter concerned became extremely irate that although they had registered properly, the system seemed to have let them down.
Nor did there seem to be any way of redressing the problem.
Flustered police and officials tried to calm the voters down but their only advice was to go to voting stations where full lists were kept.
So these unlisted voters faced a frustrating hunt for their names on lists apparently scattered around the city.
"It is a shame that this problem is happening in an otherwise smoothly-run election," a Swedish MP who came to monitor the election told the BBC.
However, the main issue for most voters has been freedom of movement under the restrictions placed on Palestinian areas by the occupying Israeli army.
Down at Kalandia checkpoint, on the route between Ramallah and Jerusalem, there was very little sign of delays for people crossing this permanent roadblock.
Election NGOs have been out in the streets encouraging people to vote
But although Israel had promised to allow Palestinians through, as long it its security was not compromised, Kalandia was not open to everyone.
The usual restrictions seemed to be in force, that only Ramallah residents could use it, and any residents from the northern or southern West Bank - perhaps to vote in their home towns - had to find other ways round.