But the Americans have been involved in fierce fighting against Iraqis in some areas and they say Saddam's best troops, the Republican Guard still had "great potential for some sharp fights"
The Americans say they're now pushing from at least three directions to take control of more of Iraq's capital.
Troops in the centre are hoping to link up with troops from the other units in the south-east and north-west of the city.
Marines have advanced onto a military airbase in the south-east of Baghdad and the US military say they have control of all the major roads into the city.
But there are also reports that hundreds of people are trying to leave and escape the fighting.
Other main points:
US military officials assess whether a raid on a residential area of Baghdad designed to kill Saddam Hussein was successful. UK forces say he escaped.
The Red Cross says the hospitals in Baghdad are overwhelmed, they can't cope and they have no water or electricity
Three journalists are killed in central Baghdad, two after the Palestine Hotel is hit.
British soldiers in the southern city of Basra say they need to make it more secure before they can deal with the widespread looting.
US President George Bush and UK Prime Minister Tony Blair have said they both want to involve the United Nations in rebuilding Iraq after the war.
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