IN HIS briefings to journalists in Baghdad, US Military spokesman Major General Rick Lynch regularly displays slides showing the face of Abu Musab al-Zarqawi, the head of al-Qaeda in Iraq, and America's most wanted man.
Posters of the Jordanian-born terrorist, whose organisation has claimed responsibility for many killings, including beheadings, dominate almost every US barracks and checkpoint.
Yet the video that surfaced last week showing four Western hostages, including retired British professor and peace activist Norman Kember, originated from a group that was completely unknown.
The Swords of Righteousness Brigade must now be added to around 100 insurgent groups operating in Iraq.
The challenge facing the US and its allies, including Britain, has been totally transformed by the fact that the insurgency no longer conforms to the stereotype according to which al-Qaeda is perceived as planning and carrying out attacks throughout Iraq in a coordinated campaign.
A Washington group, the Search for International Terrorist Entities (SITE) Institute, which collates information on insurgency groups that use the internet, has identified more than 100 claiming to be waging jihad in Iraq.
They have fierce-sounding and evocative names, such as Al Baraa bin Malik Suicide Brigade, The Tawid Lions of Abdullah ibn al Zobeir, Supporters of the Sunni People, The Men's Faith Brigade and Islamic Anger. New ones appear almost daily.
While some claim affiliation with al-Qaeda in Mesopotamia, the title which al-Qaeda gives itself in Iraq, others appear to act alone.
Last week in a major speech ahead of the December 15 election in Iraq, President George Bush said he would not accept "anything less than complete victory".
But in a notable change of tone, Bush, whose popularity in the polls is spiralling downwards because of Iraq, said American troops would increasingly move out of Iraqi cities, reduce the number of bases from which they operate and conduct fewer patrols.
The Bush administration has long maintained that the insurgency is made up of three groups: disaffected Sunni Arabs, who have lost out since the fall of Saddam; former Saddam government loyalists; and foreign-born terrorists connected to al-Qaeda.
But the proliferation of insurgency groups explains why the insurgency has been so hard to destroy, forcing the US to change tack.
Last week, even though the Americans were able to announce that suicide bombings fell in November to their lowest level in seven months, the trend has not resulted in less bloodshed: 85 US troops died during the month, one of the highest tolls since the invasion.
On Thursday a roadside bomb killed 10 Marines and wounded 11 near Falluja in the deadliest attack on American troops in nearly four months. The bomb, made from large artillery shells, went off near a foot patrol. A US Army soldier assigned to the Marines also died in a separate attack near Ramadi. On Wednesday, four American service members were killed. The total number of US military killed in Iraq is now at least 2,121. The Iraqi troops meant to replace them are also dying: yesterday 19 were killed in a roadside bomb northeast of Baghdad.
"There is no centre of gravity, no leadership, no hierarchy; they are more a constellation than an organisation," says Bruce Hoffman, a terrorism expert at the Rand Corporation of the new-look insurgency. "They have adopted a structure that assures their longevity." As a result, even killing or capturing al-Zarqawi would not end the rebellion.
Because the structure of the Iraqi insurgency is horizontal as opposed to hierarchical, it cannot be decapitated. Most of it remains untouched and carries on after any single part of it is attacked.
Highly visible and well-known groups such as al-Qaeda, Ansar al Sunna and the Victorious Army Group are still powerful in Iraq. Of the groups found by SITE, 59 are claimed by al-Qaeda and 36 by Ansar al Sunna. Eight groups claim to be operating under the direction of the Victorious Army Group, and five groups say they are operating under the 20th of July Revolution Brigade.
The "majors" act as fronts, officials say, providing money, direction and expertise to smaller groups, and then taking responsibility for their attacks by broadcasting them on the internet afterwards.
"The leaders usually don't have anything to do with details," says Abdul Kareem al-Eniezi, Iraq's minister for national security. "Sometimes they will give the smaller groups a target, or a type of target. The groups aren't connected to each other. They are not that organised."
To complicate matters further, larger groups will sub-contract to smaller ones. Ansar al Sunna recently sub-contracted an attack to the Al Baraa bin Malik Suicide Brigade, which ambushed and killed six Marine snipers who were moving on foot near the Western Iraqi city of Haditha. Taking responsibility for the attack, Ansar al Sunna said that its men, whom it called the Lions of Monotheism, had carried out the attack against the "crusader convoy".
After a coordinated attack by three suicide bombers on the Sheraton and Palestine Hotels in Baghdad in October, which killed 12 people, al-Qaeda, while claiming responsibility in an internet posting, declared that the attacks had actually been carried out by three separate groups: the Attack Brigade, the Rockets Brigade and Al Baraa bin Malik Suicide Brigade.
There is growing evidence of turf wars among the groups. On the streets of Ramadi, the violent city west of Baghdad, a leaflet found on the street, signed by a group called the Islamic Army, said that "the growing number of mujahedeen groups, which grew in number when the people realised their value", had caused confusion about which group was speaking for which.
Some groups have formed alliances of convenience. Others simply carry out attacks based on ethnic hatred. A group calling itself the Supporters of the Sunni People says that its members killed 15 Shi'ites at a fake checkpoint it had set up on a highway south of Baghdad. Its website posting says the insurgents stopped cars and pulled out Iraqis who appeared to be members of Shi'ite militias. "More than 15 Shia who were proven to be related to the parties who support the crusaders in Iraq were killed," the posting said.
Others are just private murderous mafias that thrive in the atmosphere of lawlessness that prevails in large parts of the country. A study by the Washington-based Centre for Strategic and International Studies concluded that there were around 30,000 insurgents, of whom between 4% and 10% were foreign. It said that the largest contingents were Algerians (20%), Syrians (18%), Yemenis (17%), Sudanese (15%) and Egyptians (13%).
They can be hard to distinguish from the general population, the report says, because cell leaders have encouraged them to shave their beards, which symbolise piety, and to carry cigarettes, even though most do not smoke.
"Both Iraqis and coalition people often exaggerate the role of foreign infiltrators and downplay the role of Iraqi resentment in the insurgency," said Anthony Cordesman, a former Pentagon official, who is co-author of the study. "It makes the government's counter-insurgency efforts seem more legitimate, and it links what's going on in Iraq to the war on terrorism."
IN THE British-controlled zone around Basra, however, it is hard to overestimate the power of foreign influences on the local population, but here too the war against the insurgency is going badly.
The border with Iran is highly porous, and the dominant local Shia population is naturally sympathetic to its co-religionists that rule the Islamic Republic. Faced with increasing evidence that Iran is either organising or at least tolerating the smuggling into Iraq of sophisticated roadside explosive devices, British troops are having to be more ruthless.
British special forces have embarked on a secret war using the latest sophisticated technology to find and kill would-be suicide bombers. According to recent reports, the SAS are using satellite tracking devices to pinpoint and kill suicide bombers as they utter their final prayers before planting their bombs.
But the row that followed the capture of two undercover SAS men in September, and the subsequent rescue operation using armoured vehicles, has heightened hostility against the British among the Shias, who had previously shown signs of acceptance.
The fragmentation of the insurgency may also explain the latest wave of hostage-taking, which has seen more than a dozen civilians taken, including Professor Kember. The abductions give militants the high-profile publicity they seek to show they are still a force to be reckoned with.
"The media card is crucial in any international conflict, and these groups are seeking to reaffirm their existence through such kidnappings," says Diaa Rashwan, an Egyptian expert on Islamic militancy.
As the Iraqi parliamentary elections of December 15 loom, the insurgents are expected to step up their attacks. There will doubtless be more dead soldiers, and more Norman Kembers.