Contenders:
- Ahmad Chalabi is one of the best-known figures. He leads the Iraqi National Congress (INC), which has been backed by the US and Britain ever since it was created in the aftermath of the last war against Iraq, in 1991. He has the support of the Washington hawks, who believe he is the man to set Iraq on a democratic path. His critics, however, point out that he left Iraq in the 1950s and has been accused of corrupt business dealings. As a (secular) Shia he arouses the mistrust of the Arab world's Sunni ruling class.
- Ayatollah Muhammad Baqr al-Hakim, who is from a prominent Iraqi Shia family, runs the Tehran-based Supreme Council for the Islamic Revolution in Iraq (SCIRI). He has supporters in Iraq, but the Iranian connection makes the US - and some Iraqis - wary of him.
- Adnan Pachachi, a former Iraqi foreign minister, is an 80-year-old Sunni who has been courted by the Americans and is well connected in the Gulf sheikhdoms. He is a nationalist with a secular liberal outlook. Some see him, because of his age, as a possible caretaker leader.
- Jalal Talabani and Massoud Barzani, the leaders of the two Kurdish factions in northern Iraq, have a firm base among their own people but would be unlikely contenders for national power.
- Nizar Khazraji, a prominent Iraqi general who defected to the West, is sometimes mentioned as a possible successor to Saddam. The CIA is reported to have helped him escape to the Gulf from house arrest in Denmark, where prosecutors were investigating his alleged role in gas attacks on the Iraqi Kurds.
Washington infighting
In the absence of a candidate with impeccable credentials, the US may try to build up a collective leadership - one which would represent Iraq's mosaic of different communities and command enough confidence to return the country to some sort of normality.
But it is not only within Iraq that fierce differences over the post-war future are being played out.
In Washington, the State Department and the CIA suspect the Pentagon of actively promoting its protege, Ahmad Chalabi, who was recently flown into southern Iraq by the US military with a group of his followers.
They fear that imposing Mr Chalabi would alienate other Iraqis.
The White House has tried to damp down the infighting. But the dispute is unresolved.