The first round took place on 28 May, but no candidate reached the 40% threshold to win outright. Louisa Brooke, Middle East analyst for BBC Analysis and Research, profiles the frontrunners and the outgoing leader.

Ehud Barak - (first round share of vote 36%)

Ehud Barak served as Prime Minister from 1999 to 2001, when he was beaten by Ariel Sharon in a direct election for the prime minister's position.

His tenure as Prime Minister is probably best remembered for his decision to pull Israel out of south Lebanon. He unilaterally withdrew the Israeli Defence Force after nearly 20 years.

It is also remembered for the Camp David talks in summer 2000. Then President Clinton brought Barak and PLO chairman Yasser Arafat together for marathon talks in the US.

There was no agreement but negotiations were very detailed. The Palestinian uprising, or intifada, broke out several months later.

Barak held talks with the Syrian Foreign Minister in Shepherdstown, America, in January 2000. Clinton and Assad met in Geneva to continue negotiations, but talks stalled. Syrian President Assad died in June 2000.

Mr Barak entered the Knesset in 1996 and served in various ministries, including foreign and defence. After his 2001 defeat he worked in the private sector.

This is not the first time he has tried to regain the Labour leadership. He briefly ran for the 2005 leadership only to pull out and declare his support for Shimon

Mr Barak was born in 1942 and joined the Israeli army in 1959, serving for 35 years. He famously disguised himself as a woman during one operation to assassinate PLO members in Beirut.

He rose to become Chief of the General Staff and is Israel's most decorated soldier. He is also an expert in Krav magra, the official martial art of the IDF.

He is separated with three daughters.

Ami Ayalon - (first round share of vote 31%)

Ami Ayalon has a strong military background. He served in the navy and received Israel's highest military award for his part in a raid in 1969.

He headed the navy's elite special forces unit before rising to commander in chief of the Navy between 1992 and 1996.

He was the first person outside Shin Bet, Israel's internal security agency, to be appointed as its director. He spent four years in charge until he left in 2000.

In 2003 he co-wrote a peace statement called "the People's voice" with Palestinian academic Sari Nusseibeh. The proposal calls for two states for two peoples and offers solutions to the problems of Jerusalem, borders and Palestinian refugees.

During the Labour leadership campaign Mr Ayalon called for a regionalisation of the Israeli-Palestinian conflict.

Mr Ayalon joined the Knesset in 2006 as a member of the Labour party. He sits on a number of committees but has not had any cabinet positions.

He was born in 1945 and is married with three children.

Amir Peretz - (first round share of vote 22%)

Amir Peretz was heavily criticised for his role as defence minister in the war in Lebanon last summer by an internal Israeli report.

The Winograd Commission, in its first report on the war, concluded that the "Minister of Defense did not have knowledge or experience in military, political or governmental matters". It also said "the Minister of Defense failed in fulfilling his functions".

Polls suggested that more three-quarters of Israelis thought Mr Peretz should resign after the report came out.

Earlier this year Israeli newspapers printed a picture of Mr Peretz looking through binoculars with the lens cap on, for which he was widely ridiculed.

Mr Peretz was elected leader of the Labour party on 9 November 2005, beating Shimon Peres.

He was born in Morocco in 1952 and immigrated to Israel aged four with his family, who settled in the town of Sderot, just outside the borders of Gaza. He was hospitalised for two years after being injured while serving in the military, after which he became a farmer.

He joined the Knesset in 1988 as a member of the Labour party but broke away in 1999 to set up the Am Ehad (One Nation) party. The latter has now rejoined the Labour party. He also led the Histradrut Labour Federation, the largest trade union in Israel.