Palestinian Prime Minister Ahmed Qurei has resigned from his job following the elections held on Wednesday.
Although the final result has not been confirmed, it looks like Islamic organisation Hamas have taken lots of seats from the ruling party Fatah.
Mr Qurei says Hamas should form the next government. The final election result is expected later on Thursday.
Israel, the US and the EU consider Hamas a terrorist group and have said they do not want to work with them.
Hamas want the Palestinian people to be given their own land, but the land they want is occupied by Israel.
The group say it will never accept the state of Israel, and has used violence in the past.
There have been clashes between Hamas and Fatah supporters in Ramallah. Shots have reportedly been heard, and some people have been injured.
Once the final election result is announced, it is likely that Hamas and Fatah will form a joint government made up of both parties.
Fatah has been the ruling party in Palestinian politics for many years, and was formed by former Palestinian leader Yasser Arafat who died in 2005.