What is civil war? The question is often raised about the disorders in Iraq. Does the violence between Iraqi religious and political factions amount to civil war, or is it best described another way? The US-led coalition's spokesmen, echoing the views of the White House and Downing Street, refuse to call the disorders civil war. Presumably they believe that to do so would be to admit defeat in their project to set up a stable, legitimate new Iraq.

To assess the situation in Iraq, it is helpful to understand how a civil war differs from an inter-state, cross-border war. There are three principal defining aspects of a civil war, each with numerous subsidiary requirements. The basic formula is simple: the violence must be "civil," it must be "war," and its aim must be either the exercise or the acquisition of national authority.

The "civil" part of the definition means the struggle must be conducted within a national territory, and that it must be carried on largely by the people of that territory, fighting between themselves. It must also involve a significant degree of popular participation.

A civil war also has to be a war—what the dictionary calls a "hostile contention by means of armed forces." Does this definition 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 the combatants. The battles do not have to be organised, in other words, but the people do. A civil war requires leaders who say what they are fighting for and why, and a public that understands what it is all about—the divisions, the people and the goals.

The third principal condition, authority, is just as important. The point of the violence must be sovereign rule: combatants must be trying either to seize national power or to maintain it. This is the difference between, for example, the Russian civil war and the tribal rebellions now taking place in 14 of India's 28 states, or the late 1990s insurgency of Subcomandante Marcos in Mexico. Revenge, struggles for rights, mass criminality and positioning for economic gain are not sufficient, individually or severally. The opponents must be fighting to rule.

To pass the test of posterity and achieve historical status as a civil war is extremely 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 are, of course, thousands of other violent internal struggles in history. But few are remembered as civil wars. Some of those that are so remembered have been misnamed, at least according to our criteria. (The Irish civil war is a borderline case and depends on the extent to which the free-staters are judged to have been running the state.)

When did civil war, as opposed to mere faction fighting between rivals for power, first make an appearance? The English wars of the roses of the 15th century are a possible starting point. These conflicts, however, were largely carried on by landed warriors, allied by family connection to one or other of the principals. The common people did not take part, and indeed were actively deterred from doing so. The wars of the roses thus were not civil wars but violent power struggles. They were brought to an end by the death in battle of the King of England, Richard III, at the hand of his rival, Henry Tudor, who became Henry VII.

But the wars of the roses did have one important ingredient of civil war: the principle of legitimacy. Henry Tudor fought with the determination he did because he believed he had a right in law to the throne of England and because, with reason, he regarded Richard III as a usurper. He nevertheless succeeded by right of conquest alone, and his dynasty kept the throne in subsequent reigns by military force.

The succession passed from the last of the Tudors, the childless Elizabeth, to the Stuarts, whose misrule was challenged on grounds of legitimacy by the parliamentary faction, eventually led by Oliver Cromwell. Cromwell invoked legitimacy to justify his usurpation but it was legitimacy in a new form: ideological rather than hereditary. Cromwell believed that the crown of England could be worn only by a king who was approved by parliament. Charles Stuart's rejection of that view led to the English civil war.

This first civil war reveals all the marks of a classic: claims to legitimacy by both sides, based partly on inheritance and partly on ideology, with the aim of ruling over the whole; the involvement of the common people; the taking of sides by a divided political class; formal military engagements; and the use of violence against the defeated ruler. There was an element of revolution, too, as the victors attempted to institutionalise their victory by bringing about social as well as political changes. The aim was a "new" England, represented by true believers who inherited control of key institutions with the object of changing the country's belief system. Important changes of lasting effect were brought about by the English civil war, though many of these were reversed when divisions within parliament led to the restoration of the Stuarts in 1660.

The war had the effect of inoculating the English against going to war ever again in the name of politics. We might have invented civil war, but we have seen nothing like it since. In that sense, the English civil war was deeply important and highly successful.

Many of those who took part in the American civil war regarded it as being conducted in the spirit of the English civil war (the notion of the "cavalier" was especially alluring to the gentleman soldiers of the confederacy, epitomised by the dashing cavalry chief JEB Stuart). The American conflict, like its predecessor, was fought over an issue of political authority but with an undeclared purpose of social transformation, in this case the abolition of chattel slavery. It was truly a civil war in that common people were hugely involved. In its intensity and totality, it anticipated the big civil wars that were to follow in the 20th century. It was distinguished from them, however, by the spirit of magnanimity that for the most part characterised the conduct of the victors.

By contrast, the Spanish civil war of 1936-39, fought over deep divisions in Spanish society, was characterised by extreme brutality and then savage revenge exacted by the victors. Beginning as a military revolt against the government, in protest at its hostility to certain traditional features of Spanish society, particularly the Catholic church, the conflict was deliberately prolonged by General Franco, the leader of the revolt, so as to inflict as many casualties as possible. Thus it was at terrible cost to Spanish society that the war achieved its objects. It exhibited one feature that was to become common in later civil conflicts: the attraction of foreign fighters sympathetic to the ideas of one side or the other.

The Russian civil war of 1918-21 was an outright ideological struggle, inaugurated by the Bolsheviks to establish communist rule throughout the former czarist empire. It was characterised by brutality on both sides, the intervention of outsiders, and the taking of revenge. Leaders were executed and terror was used against civilians on both sides. It was territorial, it was domestic and it involved large numbers of the common people fighting for both sides. It was ideological and about legitimacy, and led to revolution.

Apart from attacks on the US-led coalition, the current violence in Iraq shows two signs of civil war: it is taking place within the national boundaries of a single country, and it primarily involves local people killing local people. It is civil, in other words. But is it war? And what about the question of authority?

There are three major categories of player in Iraq's domestic violence, each of which has important internal divisions. The Sunni insurgency dominated the violence until spring of this year, when its bombing of the mosque at Samarra finally delivered the long-standing goal of goading Shias into large-scale reprisals. The Sunni violence is composed of two principal parts, one motivated by hardcore Wahhabist and Salafist Islam, and the other by the secular outlook of Baathism.

The second main category is the Shia militias. The most dangerous and active of these is the Mahdi army associated with Muqtada al-Sadr, a fractious and nebulous phenomenon that includes many groups whose connection to the movement is nominal. The older and less active—though better organised—Shia militia is the Badr Organisation, formed during the Shia struggle against Saddam, and originally trained and based in Iran. Badr belongs to Sciri, one of Iraq's two main Iranian-backed political parties and is almost always at odds with the al-Sadr movement, which derives its popularity from Iraqi nationalism.

The third major player in the Iraqi civil killing is the tendency that fights on behalf of the Iraqi state against the sectarian agendas of the Sunni insurgency and the Shia militias. The Iraqi police, police commandos and other ministry of interior forces have been heavily infiltrated by the militias, especially the Mahdi army. The Iraqi army is far more independent. With almost 500,000 Iraqis serving with the police or army, it seems safe to say well over 100,000 Iraqis are fighting for the state against the militias and the insurgents. They represent a major armed faction whose agenda is the preservation of a unified, secular and pluralistic state.

The most striking feature of the civil violence in Iraq is that it is for the most part decidedly unmilitary. Despite the names of the two Shia militias, only the third group, the state forces, exhibits the military characteristics of the principal actors in the five conflicts that we recognise as civil wars: uniforms, clear chains of command, acknowledged leadership, and official, public war aims.

There are no, or almost no, battles in Iraq's domestic killing. Civilians are the principal targets. The looser definition of the "war" part of civil war nonetheless acknowledges that if factions or regions are killing enough people for enough time, it can be petty not to recognise the conflict as something very like a war. Iraq meets this standard only partly: the non-state players for the most part lack anything like the public character of players in civil wars to date. In other words, it is not so much that Iraq is a conflict without uniforms and fighting that prevents it from being a civil war, but rather that it is violence in which no player except the state and al Qaeda, which is a minor player, says what it wants, or indeed says that it wants anything other than the continuation of the country's elected government. (One Sunni Islamist group has recently called for a separate Sunni state.)

An important feature of the conflict in Iraq is the lack of public rhetoric against the enemy by popular leaders. All of Iraq's leaders call constantly for unity, tolerance and an end to the violence. This was far from the case with Lenin, Franco, Cromwell or even Lincoln. To the extent that Iraq's violence 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 should they move to formalise this status, no Arab Iraqi player will be strong enough to stop them.)

Could Iraq be the first civil war ever without battles, generals, explicit war aims, the use of partisan public rhetoric by civilian leaders, mass public participation and targets of a predominantly military nature? Even if Iraq today possessed these characteristics, it would still lack something even more important: the struggle for authority. In Iraq, the state actors are fighting for authority. But the others are not, which is probably why we do not hear from them. The Shia militias are the armed wings of the two biggest parties in parliament, and their people own the top ministries. Neither Badr nor the al-Sadr movement is big enough or strong enough to own the state itself. They balance each other while the Sunnis, whose violent actors are far smaller, provide the final guarantee against a full grab for power by either. It is no coincidence that the only player, apart from the state, that acknowledges war aims is the only player whose war aims constitute the traditional aspiration of exclusive control: the religious element of the Sunni insurgency. The aspiration to a new Baghdad caliphate frees the Wahhabis and Salafists from the pragmatic calculations of al-Sadr or the Baathists, and lets them dream of control, and talk about it on their websites.

Objectively, it must be concluded that the disorders in Iraq do not constitute a civil war but are nearer to a politico-military struggle for power. Such struggles in Muslim countries defy resolution because Islam is irreconcilably divided over the issue of the succession to Muhammad. It might be said that Islam is in a permanent state of civil war (at least where there is a significant minority of the opposing sect) and that authority in Muslim lands can be sustained only by repression if the state takes on a religious cast, since neither Shia nor Sunni communities can concede legitimacy to their opponents.

The Lebanese civil war of 1975-90 offers perhaps the closest example of the sort of outcome towards which Iraq might be heading. An Iraqi civil war, with seven main factions (pro-Iranian Shias, nationalist Shias, Islamist Sunnis, Baathist Sunnis, pro-state secularist forces, and two major Kurdish mini-governments), would very likely offer the confused and confusing array of shifting allegiances and foggy front lines that characterised much of the Lebanese conflict. Without the clarity of blue versus grey, red versus white, or roundheads versus cavaliers, and no one faction capable of winning, the Lebanese civil war went on for 15 years and ended with a broad negotiated settlement. The factions were fighting for authority, for the most part, especially the Christian Phalange, and the others for smaller nationalist projects. Ultimately the country settled into the uneasy equilibrium touched by an endless succession of flare-ups that we know today.

Full democracies are the states least prone to violent civil disorder; autocracies are the second most orderly. It is intermediate democracies and transitional states that are the least orderly. Iraq, of course, is both a transitional and an intermediate democracy. Even without the peculiarly violent character that has been endemic to Mesopotamia since history began there 6,000 years ago, Iraq would still be in the sweet spot for chaos. Yet apart from the Salafists, the state forces are the only player in the current phase of Iraq's domestic violence that aspires to replace the current constitutional arrangement with its own sole rule. These forces, of course, are the only ones that can have that aspiration, for they are the only players who combine the various sectarian identities, and thus the only ones who possess a theory of rule that might work. The individual sectarian tendencies are too weak to replace the current constitutional order in any foreseeable scenario. So what are they fighting for? Revenge, criminality, ideology and political advantage, but not sole authority over the state.