The two no-fly zones over Iraq were imposed by the US, Britain and France after the Gulf War, in what was described as a humanitarian effort to protect Shia Muslims in the south and Kurds in the north.
The justification was that an acute humanitarian crisis made it necessary to infringe the sovereignty of Iraq in this way.
However, unlike the military campaign to expel Iraqi forces from Kuwait, the no-fly zones were not authorised by the United Nations and they are not specifically sanctioned by any Security Council resolution.
The Western powers - led by President George Bush senior - argued that their action was consistent with Security Council Resolution 688 adopted on 5 April 1991.
The resolution condemned the repression of the Iraqi civilian population and demanded that Iraq end it immediately.
It said the repression amounted to a threat to international peace and security - a phrase often used to justify intervention.
But critics of the no-fly zones point out that the resolution did not say the Security Council was acting under Chapter VII of the UN Charter, which provides for enforcement action.
Nor did it say that all necessary means could be used.
Critics add that whatever was justified in 1991 is not necessarily justified more than 10 years later, when the reasons for continuing the air patrols may have changed.
France no longer takes part in policing the no-fly zones, and the US and the UK are now alone in the Security Council in insisting that their frequent bombing of Iraqi targets is covered by international law.
Many UK ministers say that under international law, there is a right to intervene to prevent a humanitarian catastrophe.
US and UK aircraft have patrolled the zones for more than a decade
They point out that Iraqi leader Saddam Hussein has hurt his people before - when he used chemical weapons to kill 5,000 Kurdish villagers in the 1980s.
Other countries, notably China and Russia, have condemned the no-fly zones as a violation of Iraqi sovereignty, and they insist there is no backing for the policy under international law or UN resolutions.
The northern no-fly zone was declared after the end of the Gulf War in March 1991 to protect Kurds against military action which had driven huge numbers of people across the borders into Turkey and Iran.
Subsequently, the US, UK and France set up safe havens on the ground in northern Iraq, to which the refugees returned.
In a separate move, Iraqi aircraft were also prohibited from flying over the southern half of the country, in order to hamper President Hussein's operations against the Shia population there.
Latest UN resolution
Since UN weapons inspectors withdrew from Iraq shortly before a three-day US-UK bombardment in late 1998 known as Operation Desert Fox, the two Western powers have kept up their attacks whenever Iraqi air defences have locked onto aircraft patrolling the no-fly zones.
Baghdad says hundreds of civilians have died in these attacks.
The US and British air forces have disputed some of these figures, and insist they never target civilian areas.
However, the raids have provided ammunition for Iraqi efforts to garner support for an end to its international isolation.
The latest UN resolution on the disarmament of Iraq does not mention the no-fly zones, but it does stipulate that Baghdad should not take or threaten hostile acts directed against any member state taking action to uphold Security Council resolutions.
This is the most likely clause Washington will refer to if it wants to assert that firing on British and American planes amounts to a violation of the UN resolution.