Two American soldiers have been killed and eight others injured in two separate attacks on military convoys in Iraq on Wednesday, the US military says.
US troops come under daily attack in Iraq
Both assaults - one near the northern city Mosul, the other in the central town of Ramadi - involved what US Central Command described as "improvised explosive devices" exploding near American vehicles.
The Mosul attack reportedly involved an explosion detonated by remote control.
More than 40 US soldiers have died in action in Iraq since the war that toppled Saddam Hussein was declared over on 1 May.
Wednesday morning's fatalities came amid hopes that reports of the deaths of the former president's sons would sap the morale of those launching attacks on US forces.
In the first attack, a soldier from the same army division that stormed the villa in Mosul was killed when two vehicles were hit on a highway outside the city.
Seven other members of the 101st Airborne Division were wounded.
The second attack saw a soldier from the 3rd Armoured Cavalry Regiment killed on a highway in Ramadi, a town west of Baghdad in the "Sunni triangle" area of Iraq that has seen most resistance to the US-led occupation.
Another soldier and a civilian contractor were injured.
'Better days ahead'
BBC defence correspondent Jonathan Marcus says the deaths of Uday and Qusay Hussein do not mean that attacks on US forces will end.
US officials have blamed remnants of Saddam Hussein's Baath party
and Uday's feared Saddam Fedayeen militia for the attacks.
But our correspondent says the attacks stem from many motives - including criminal, nationalist and the redress of local grievances.
However, he adds that for ordinary Iraqis who may still fear a return of Saddam Hussein's regime, it is a powerful signal that better days could lie ahead.
And for those still loyal to the former regime, it is an equally powerful sign that the old order has crumbled and gone for good.
Paul Bremer, the US administrator of Iraq, has admitted that there is
a risk of revenge attacks by Saddam Hussein loyalists.
"We could see attacks in the next few days as revenge," he said.
you have to remember that a lot of the attacks that are taking
place are being based on the idea that somehow the Saddams are
coming back, that he and his sons are coming back.
"Well, they're not coming back."