I was in the police station in the town of Fallujah when I realised the extent of the schizophrenia. Captain Christopher Cirino of the 82nd Airborne was trying to explain to me the nature of the attacks so regularly carried out against American forces in the Sunni Muslim Iraqi town. His men were billeted in a former presidential rest home down the road - "Dreamland", the Americans call it - but this was not the extent of his soldiers' disorientation. "The men we are being attacked by," he said, "are Syrian-trained terrorists and local freedom fighters." Come again? "Freedom fighters." But that's what Captain Cirino called them - and rightly so.

Here's the reason. All American soldiers are supposed to believe - indeed have to believe, along with their President and his Defence Secretary, Donald Rumsfeld - that Osama bin Laden's "al-Qa'ida" guerrillas, pouring over Iraq's borders from Syria, Iran, Saudi Arabia (note how those close allies and neighbours of Iraq, Kuwait and Turkey are always left out of the equation), are assaulting United States forces as part of the "war on terror". Special forces soldiers are now being told by their officers that the "war on terror" has been transferred from America to Iraq, as if in some miraculous way, 11 September 2001 is now Iraq 2003. Note too how the Americans always leave the Iraqis out of the culpability bracket - unless they can be described as "Baath party remnants", "diehards" or "deadenders" by the US proconsul, Paul Bremer.

Captain Cirino's problem, of course, is that he knows part of the truth. Ordinary Iraqis - many of them long-term enemies of Saddam Hussein - are attacking the American occupation army 35 times a day in the Baghdad area alone. And Captain Cirino works in Fallujah's local police station, where America's newly hired Iraqi policemen are the brothers and uncles and - no doubt - fathers of some of those now waging guerrilla war against American soldiers in Fallujah. Some of them, I suspect, are indeed themselves the "terrorists". So if he calls the bad guys "terrorists", the local cops - his first line of defence - would be very angry indeed.

No wonder morale is low. No wonder the American soldiers I meet on the streets of Baghdad and other Iraqi cities don't mince their words about their own government. US troops have been given orders not to bad-mouth their President or Secretary of Defence in front of Iraqis or reporters (who have about the same status in the eyes of the occupation authorities). But when I suggested to a group of US military police near Abu Ghurayb they would be voting Republican at the next election, they fell about laughing. "We shouldn't be here and we should never have been sent here," one of them told me with astonishing candour. "And maybe you can tell me: why were we sent here?"

Little wonder, then, that Stars and Stripes, the American military's own newspaper, reported this month that one third of the soldiers in Iraq suffered from low morale. And is it any wonder, that being the case, that US forces in Iraq are shooting down the innocent, kicking and brutalising prisoners, trashing homes and - eyewitness testimony is coming from hundreds of Iraqis - stealing money from houses they are raiding? No, this is not Vietnam - where the Americans sometimes lost 3,000 men in a month - nor is the US army in Iraq turning into a rabble. Not yet. And they remain light years away from the butchery of Saddam's henchmen. But human-rights monitors, civilian occupation officials and journalists - not to mention Iraqis themselves - are increasingly appalled at the behaviour of the American military occupiers.

Iraqis who fail to see US military checkpoints, who overtake convoys under attack - or who merely pass the scene of an American raid - are being gunned down with abandon. US official "inquiries" into these killings routinely result in either silence or claims that the soldiers "obeyed their rules of engagement" - rules that the Americans will not disclose to the public.

The rot comes from the top. Even during the Anglo-American invasion of Iraq, US forces declined to take responsibility for the innocents they killed. "We do not do body counts," General Tommy Franks announced. So there was no apology for the 16 civilians killed at Mansur when the "Allies" - note how we Brits get caught up in this misleading title - bombed a residential suburb in the vain hope of killing Saddam. When US special forces raided a house in the very same area four months later - hunting for the very same Iraqi leader - they killed six civilians, including a 14-year-old boy and a middle-aged woman, and only announced, four days later, that they would hold an "inquiry". Not an investigation, you understand, nothing that would suggest there was anything wrong in gunning down six Iraqi civilians; and in due course the "inquiry" was forgotten - as it was no doubt meant to be - and nothing has been heard of it again.

Again, during the invasion, the Americans dropped hundreds of cluster bombs on villages outside the town of Hillah. They left behind a butcher's shop of chopped-up corpses. Film of babies cut in half during the raid was not even transmitted by the Reuters crew in Baghdad. The Pentagon then said there were "no indications" cluster bombs had been dropped at Hillah - even though Sky TV found some unexploded and brought them back to Baghdad.

I first came across this absence of remorse - or rather absence of responsibility - in a slum suburb of Baghdad called Hayy al-Gailani. Two men had run a new American checkpoint - a roll of barbed wire tossed across a road before dawn one morning in July - and US troops had opened fire at the car. Indeed, they fired so many bullets that the vehicle burst into flames. And while the dead or dying men were burned inside, the Americans who had set up the checkpoint simply boarded their armoured vehicles and left the scene. They never even bothered to visit the hospital mortuary to find out the identities of the men they killed - an obvious step if they believed they had killed "terrorists" - and inform their relatives. Scenes like this are being repeated across Iraq daily.

Which is why Human Rights Watch and Amnesty and other humanitarian organisations are protesting ever more vigorously about the failure of the US army even to count the numbers of Iraqi dead, let alone account for their own role in killing civilians. "It is a tragedy that US soldiers have killed so many civilians in Baghdad," Human Rights Watch's Joe Stork said. "But it is really incredible that the US military does not even count these deaths." Human Rights Watch has counted 94 Iraqi civilians killed by Americans in the capital. The organisation also criticised American forces for humiliating prisoners, not least by their habit of placing their feet on the heads of prisoners. Some American soldiers are now being trained in Jordan - by Jordanians - in the "respect" that should be accorded to Iraqi civilians and about the culture of Islam. About time.

But on the ground in Iraq, Americans have a licence to kill. Not a single soldier has been disciplined for shooting civilians - even when the fatality involves an Iraqi working for the occupation authorities. No action has been taken, for instance, over the soldier who fired a single shot through the window of an Italian diplomat's car, killing his translator, in northern Iraq. Nor against the soldiers of the 82nd Airborne who gunned down 14 Sunni Muslim protesters in Fallujah in April. (Captain Cirino was not involved.) Nor against the troops who shot dead 11 more protesters in Mosul. Sometimes, the evidence of low morale mounts over a long period. In one Iraqi city, for example, the "Coalition Provisional Authority" - which is what the occupation authorities call themselves - have instructed local money changers not to give dollars for Iraqi dinars to occupation soldiers: too many Iraqi dinars had been stolen by troops during house raids. Repeatedly, in Baghdad, Hillah, Tikrit, Mosul and Fallujah Iraqis have told me that they were robbed by American troops during raids and at checkpoints. Unless there is a monumental conspiracy on a nationwide scale by Iraqis, some of these reports must bear the stamp of truth.

Then there was the case of the Bengal tiger. A group of US troops entered the Baghdad zoo one evening for a party of sandwiches and beer. During the party, one of the soldiers decided to pet the tiger who - being a Bengal tiger - sank his teeth into the soldier. The Americans then shot the tiger dead. The Americans promised an "inquiry" - of which nothing has been heard since. Ironically, the one incident where US forces faced disciplinary action followed an incident in which a US helicopter crew took a black religious flag from a communications tower in Sadr City in Baghdad. The violence that followed cost the life of an Iraqi civilian.

Suicides among US troops in Iraq have risen in recent months - up to three times the usual rate among American servicemen. At least 23 soldiers are believed to have taken their lives since the Anglo-American invasion and others have been wounded in attempting suicide. As usual, the US army only revealed this statistic following constant questioning. The daily attacks on Americans outside Baghdad - up to 50 in a night - go, like the civilian Iraqi dead, unrecorded. Travelling back from Fallujah to Baghdad after dark last month, I saw mortar explosions and tracer fire around 13 American bases - not a word of which was later revealed by the occupation authorities. At Baghdad airport last month, five mortar shells fell near the runway as a Jordanian airliner was boarding passengers for Amman. I saw this attack with my own eyes. That same afternoon, General Ricardo Sanchez, the senior US officer in Iraq, claimed he knew nothing about the attack, which - unless his junior officers are slovenly - he must have been well aware of.

But can we expect anything else of an army that can wilfully mislead soldiers into writing "letters" to their home town papers in the US about improvements in Iraqi daily life.

"The quality of life and security for the citizens has been largely restored, and we are a large part of why it has happened," Sergeant Christopher Shelton of the 503rd Airborne Infantry Regiment bragged in a letter from Kirkuk to the Snohomish County Tribune. "The majority of the city has welcomed our presence with open arms." Only it hasn't. And Sergeant Shelton didn't write the letter. Nor did Sergeant Shawn Grueser of West Virginia. Nor did Private Nick Deaconson. Nor eight other soldiers who supposedly wrote identical letters to their local papers. The "letters" were distributed among soldiers, who were asked to sign if they agreed with its contents.

But is this, perhaps, not part of the fantasy world inspired by the right-wing ideologues in Washington who sought this war - even though most of them have never served their country in uniform. They dreamed up the "weapons of mass destruction" and the adulation of American troops who would "liberate" the Iraqi people. Unable to provide fact to fiction, they now merely acknowledge that the soldiers they have sent into the biggest rat's nest in the Middle East have "a lot of work to do", that they are - this was not revealed before or during the invasion - "fighting the front line in the war on terror".

What influence, one might ask, have the Christian fundamentalists had on the American army in Iraq? For even if we ignore the Rev Franklin Graham, who has described Islam as "a very evil and wicked religion" before he went to lecture Pentagon officials - what is one to make of the officer responsible for tracking down Osama bin Laden, Lieutenant-General William "Jerry" Boykin, who told an audience in Oregon that Islamists hate the US "because we're a Christian nation, because our foundation and our roots are Judeo-Christian and the enemy is a guy called Satan". Recently promoted to deputy under-secretary of defence for intelligence, Boykin went on to say of the war against Mohammed Farrah Aidid in Somalia - in which he participated - that "I knew my God was bigger than his - I knew that my God was a real God and his was an idol".

Secretary of Defence Donald Rumsfeld said of these extraordinary remarks that "it doesn't look like any rules were broken". We are now told that an "inquiry" into Boykin's comments is underway - an "inquiry" about as thorough, no doubt, as those held into the killing of civilians in Baghdad.

Weaned on this kind of nonsense, however, is it any surprise that American troops in Iraq understand neither their war nor the people whose country they are occupying? Terrorists or freedom fighters? What's the difference?