With Donald Rumsfeld's exit as US defence secretary, the bipartisan Iraq Study Group's report due next month and a Democrat-controlled Congress to be sworn in, hopes are high for substantial change in the prosecution of America's project in Iraq.

One question must be answered, however, before any new prescriptions: what is the nature of the violence in Iraq? If the country is mired in civil war, as many claim, it will be far more tempting to abandon it to its own savage devices. If the situation is short of civil war, the US-led coalition still has something to fight for, and the question is not whether, but how, we can help Iraq achieve a decent outcome.

The basic formula to define civil war is simple: the violence must be "civil", it must be "war" and its aim must be the exercise or acquisition of national authority. The "civil" part means the struggle must take place within a national territory, largely between the people of that territory, and must involve popular participation. A civil war also must be a war - what the dictionary calls a "hostile contention by means of armed forces". Does this require formal battles and campaigns, or does factional or regional struggle suffice? For us the baseline is a minimum degree of organisation, formality and identifiability of combatants. A civil war also requires leaders who say what they are fighting for and a public that understands what it is all about - the divisions, the people and the goals.

The third principal condition, authority, is equally important. The point of the violence must be sovereign rule: combatants must be trying to seize national power or to maintain it. Revenge, rights, mass criminality and economic gain are not sufficient motives, individually or severally. To pass the test of posterity and achieve historical status as a civil war is rare. We can think of only five clear-cut cases: the English (1642-49), the American (1861-65), the Russian (1918-21), the Spanish (1936-39) and the Lebanese (1975-90). There have been countless other violent internal struggles, of course, but few are - or should be - remembered as civil wars.

Iraq's violence shows two signs of civil war: it occurs within national boundaries and primarily involves local people killing local people. But is it war? And what about the question of authority? There are three main types of player in Iraq's domestic violence. The Sunni Muslim insurgency dominated the violence until its bombing of the Samarra mosque last spring finally goaded the Shia into large-scale reprisals. The Sunni violence comprises two principal parts, one motivated by hardcore Wahabi and Salafist Islam and the other by the gangster secularism of Ba'athism. The second category is the Shia militias. The largest is led by Moqtada al-Sadr, the radical Shia cleric. The older and less active - though better organised - is the Badr organisation. The Shia Ba'athists who formed part of Saddam Hussein's security apparatus also play a role.

The third component, Iraqi police and military, fights on behalf of the Iraqi state against the sectarian agendas of the Sunni insurgency and the Shia militias. The police have been infiltrated by the militias while the Iraqi army is far more independent. With almost 500,000 Iraqis serving with the police or army, it seems safe to say that well over 100,000 Iraqis are fighting for the state against the militias and insurgents.

A key feature of Iraq's violence is the lack of public rhetoric against the enemy by popular leaders. With the exception of the Salafists, who lack support, they call constantly for unity, tolerance and an end to the bloodletting. Without calls to upend the basic constitutional dispensation, Iraq's violence thus far fails the "authority" test. To the extent that Iraq's conflict involves separatist and regional tendencies, the lack of any public aspect to the factional desires extends to an absence of explicit territorial ambitions. The Kurds do not feature much in Iraq's civil war scenario. They are essentially separate from the Arab Iraqi state and if they move to formalise this status, no Arab Iraqi player will be strong enough to stop them. By historical standards the disorders in Iraq fall short of civil war and should be seen as a combination of extreme factionalism and massive criminality. Such struggles can defy resolution in a Muslim country because Islam itself is divided over the issue of the succession to Mohammed.

Should the forces pushing Iraq towards civil war succeed, the likelihood of an acceptable outcome in 10 years' time - of a unified Iraqi Arab state with moderate internal violence and a smooth electoral cycle - will be far less likely and that is why the US-led coalition will not leave unless things get much better or much worse.

Iraq's strategic importance is unquestionable. Its people have demonstrated great courage and tolerance since 2004, voting in huge numbers three times last year and refusing so far, despite the worst provocations, to descend into civil war or mass communal strife. Iraq matters and its people have shown they deserve a chance; new policies must recognise that once the country descends into true civil war, it will be too late to help.

Sir John Keegan, a former Sandhurst lecturer, is author of The Iraq War, and A History of Warfare (Pimlico); Bartle Bull is foreign editor of Prospect magazine. His next book is Paradise Lost (Grove/Atlantic). Their article is based on an essay in the new issue of Prospect, www.prospect-magazine.co.uk.