Residents of Rafah in the southern Gaza Strip described the day as a festive occasion as they used their votes to elect a new Palestinian president to succeed Yasir Arafat.
Samir Abu Shammala, Aljazeera's correspondent in Rafah, reported that many of the city's residents headed to the 26 electoral centres to cast their votes.
The central elections committee is supervising the process, along with international and local observers. Examiners are checking the ID cards of the voters and marking their fingers with ink to avoid any violations or duplication of votes, Abu Shammala said.
One Rafah voter said: "This is an opportunity for us to change our life. We all hope our living situations will improve. People hope their economic, social, political and security conditions will get better."
No trouble has been reported at polling stations in the West Bank, Israeli-occupied Arab East Jerusalem and the Gaza Strip.
The situation was calm in Ram Allah, where an Aljazeera correspondent reported there were no violations. All polling booths opened in the West Bank with out any problems.
Although Hamas was boycotting the election, Shaikh Hassan Yusif, a senior Hamas activist in Ram Allah, said: "We, Hamas, observe the election process like every other Palestinian citizen does, as we are a part of the Palestinian people, living all their life events.
"We have previously announced we will not participate in the presidential elections, but we will respect the choice of our people, particularly as they are eager to reach their freedom and liberty from the occupation. We will back their choice."
Early results of the elections are expected to be announced around midnight on Sunday, two hours after ballot boxes are closed. Official results will be announced Monday.