By Jonathan Marcus
BBC defence correspondent
You could call it the war after the war, though the insurgency confronting US forces is really two wars, two campaigns.
One is directed against US and coalition soldiers. Its tempo rises and falls as tactics on each side change and adapt to the latest threat.
But then there is the second campaign, that being waged by shadowy organisations against the Iraqi civilian population, or at least its Shia majority.
US forces are facing insurgency on two fronts
One wants to loosen the grip and weaken the resolve of the occupying forces, the other aims to sow division, possibly even civil war.
The invasion of Iraq by US and British forces was swift and decisive. It went far more quickly than many, even many US planners, had imagined. And the Iraqi armed forces, indeed the whole edifice of the Iraqi state, collapsed like a house of cards.
In some places, there was, briefly, serious resistance. Irregular fighters loyal to Saddam Hussein's regime contested a number of towns as US forces advanced. This, some feared, was a prelude to what might happen at the gates of Baghdad.
But, in the event, there was no "Stalingrad on the Tigris", the Iraqi collapse was complete.
Huge numbers of Iraqis are in training
It may be that the Iraqi collapse was far too complete. Pentagon planners clearly expected to be able to inherit some kind of working government. Instead they have had to create one afresh.
Now it looks as though coalition troops will be in Iraq for some considerable time. It is certainly true, as US spokesmen are always quick to insist, that this is a coalition. Well over 30 countries are represented on the ground, although the bulk of the forces are American. That will continue to be the case, whether or not Spain pulls out and whether or not there is a new UN resolution altering the status of the forces there.
If the Americans want to reduce their numbers, and they would clearly love to bring significant numbers of troops home, then they are going to have to look to local Iraqi forces, not their Nato allies, to pick up the slack.
Huge numbers of Iraqis are in training. There are troops, border guards, police and so on. Attacks against recruitment centres and individuals do not seem to have diminished the numbers of those willing to sign up. This is, after all, a real, paid job in a country that is suffering massive dislocation.
But how capable these local forces will be in shouldering the security burden is an open question. At any rate it will be a gradual process.
Iraq troop deployment is putting strain on the US army
So, people ask, can the US maintain its commitment for however long is necessary? Absolutely, just as long as the American public is willing to accept the steady drip, drip, of casualties.
As the tough-talking US Defence Secretary Donald Rumsfeld put it the other day, if America cannot sustain a deployment of 120,000 in Iraq from an overall force of over two million, then something is very wrong in the Pentagon.
Is there strain? Yes of course. Are families (read voters) worried? Yes of course. Will this be an election issue? Yes indeed, but quite how it will play in the election is hard to say.
Americans tend to conflate Iraq and the war against terrorism far more readily than the European public does. And it may be that the bomb attacks and renewed threats of terrorism in Europe will convince many American voters that for all the problems on the ground, the current strategy (read the "Bush" strategy) in Iraq is the only one available.
Senator John Kerry's problem is to convince voters that there is an alternative approach which is equally firm and resolute. And, in fact, in terms of the options in Iraq itself it is hard to see how a Kerry administration would differ from a Bush Mark II.