Gavin Hewitt sent this report for BBC News Online from a US armoured vehicle at the head of a column ploughing northwards across the Iraqi desert:
After 12 hours the convoy reached the Basra-Baghdad highway, a third of the way to Baghdad, and 3rd Infantry then began an attempt to take the strategic city of Nasariyah.
Thousands of vehicles sweep through the desert
There has been quite a lot of fighting, with rockets and artillery being fired into and around the city.
If we do go in tonight it will be the first major city to fall to American forces.
So far only minor weapons have been used against us.
No artillery has been fired by the Iraqis at units approaching the city - we do not know why that is, whether they have decided not to fight, or whether there is something that lies ahead.
The firepower which 3rd Infantry has aimed at Nasariyah has been very substantial and would have been quite intimidating.
US Infantry convoy flies the flag
On our long drive to the city across the desert all we saw was a few Iraqis tending goats and a camel train.
The column of armour was an impressive sight - lights dimmed, and just little red pencil lights on the vehicles in front.
The column stretched back for several kilometres.
The US 3rd Infantry division said when they crossed into Iraq there would be 10,000 vehicles. Not all of them were in this column, but it gives some idea of the scale.
I suspect there have been few tank drives or forward pushes in history on the scale and at the pace of this one.
I think part of the intention is to persuade the Iraqis of the enormity of the American power and convince them that there is not much purpose in resisting.
We pushed through a hole in the barbed wire marking the end of the demilitarised zone in Kuwait, then passed huge sand dunes and a giant trench which Saddam Hussein's forces had built and which has since been filled in.
We stayed in a column probably for a couple of hours until the desert opened up and then the tanks and fighting vehicles began to disperse into a formation, four-kilometres wide.
Apart for an hour's refuelling, when big tankers came up as soon as we stopped, we were pushing on at a pace through the desert.
No sign of Iraqis
Several times we passed through what appeared to be military camps, and blackened pieces of equipment and armed personnel carriers that had clearly been hit during previous air strikes - during Desert Storm in 1991 perhaps.
We also passed through one area where leaflets had been dropped by US-led forces, but if there were any Iraqi soldiers there, they had certainly left by the time we went through.
Our column is made up principally of Abrams and Bradley fighting vehicles.
Occasionally when we stopped or slowed I looked back and saw on either flank tanks and fighting vehicles stretching back for many miles.