The Iraq war proved short with a minimum of casualties among both Coalition forces and the Iraqi people. Despite this, it inflicted great damage on the institutions that helped stabilise the world during the Cold War, including history's most successful alliance, the North Atlantic Treaty Organisation.

The diplomacy that preceded the Iraq war and the campaign itself revealed fundamental differences of political views among the Alliance's pillars, France, Germany, the United Kingdom and the United States. It also exposed deep differences among the European powers and between the larger and smaller European countries. These differences will not soon be mended.

The Iraq war also revealed the unprecedented military power of combined forces trained to NATO standards. The battlefield performance of Coalition forces in Operation Iraqi Freedom was nothing less than stunning. They operated almost seamlessly in combat and transitioned easily to post-combat stabilisation operations. Indeed, both sorts of operations were conducted simultaneously. Smaller Coalition contingents, such as those from Australia and Poland, were slotted into important supporting roles without the mishaps that historically have plagued combined military operations. But for years of training within NATO, the Coalition could never have succeeded in defeating the Iraqi army and removing the regime of Saddam Hussein in less than one month.

In the aftermath of the Iraq war, Washington is beginning to understand that even the world's sole super power needs help. Institutionalising the current Pax Americana - or whatever name best suits today's international order - is unavoidable. Guaranteeing the global order "unilaterally" is not a realistic option. The question, for Americans, therefore, is whether and how to adapt NATO to fit new strategic circumstances.

The question before the Alliance is whether the current geopolitical differences will destroy NATO's abilities to provide the military basis for future coalition operations. There is a multitude of possible answers. The political differences may yet be solved, or at least be better managed. The value of the Alliance as a "force provider" may be so great that the political differences can be ignored. Conversely, the growing capabilities gap between the United States and the rest of the Alliance may exacerbate the political differences.

The answer will, in large measure, depend upon US policies and programmes in the next few years. Change is coming, and the United States and its closest partners within the Alliance will either lead the reforms that enable NATO to adapt to the "post-Cold-War" world to become a partner in the Pax Americana, or the Alliance will wither. If Washington allows NATO to wither, it will have to create some other institutional basis to underpin future "coalitions of the willing". No matter how good the US military has become, it remains a small force. Indeed, one consequence of the "capabilities gap" is that the burden of securing today's liberal international order falls more heavily on the United States, increasing the likelihood of military overstretch.

Mending the geopolitical rift between the United States and "Europe" - meaning primarily France, Germany and continental public opinion – will take time. Two issues divide us: how to deal with the problems of the Islamic world and the circumstances in which military force can appropriately be used.

Many Europeans, like some Americans, have had trouble keeping up with the change in US policy and strategy since 11 September 2001. Since then, President George W. Bush has articulated a new sense of national mission, that has gradually matured into a formal "Bush Doctrine", best regarded as a renewed sense of purpose for US power in the world. After a decade of drift and uncertainty, the Bush Doctrine represents a fundamental fork in the road of US policy and it will not be easy for future presidents to backtrack. The United States is now committed to an active form of global leadership and has embarked on an ambitious endeavour to remake the political order in the Middle East, that will be impossible to renounce without conceding defeat.

Many Europeans are still far from sharing this emerging US sense of mission or from formulating any European corollary to the Bush Doctrine. The pace of events – or perhaps more accurately, the pace of change in international politics – has at times seemed dizzying to European leaders and general publics alike. The resolution and clarity of President Bush's leadership, so comforting to Americans in a time of crisis, is disturbing to many Europeans.

Moreover, the ease of the two military victories in Afghanistan – the "graveyard of empires" – and in Iraq has been yet another reminder of the strengths of US military forces and, by contrast, the relative weaknesses of European arms. "America", wrote British scholar Timothy Garton Ash after Afghanistan, "has too much power for anyone's good, including its own." In Iraq and in the Middle East, observed François Heisbourg, perhaps France's foremost expert in security matters and generally sympathetic to US concerns, "The French, like most Europeans, don't want to give carte blanche to the Americans."

The connections made by President Bush – and accepted by most Americans – between terrorism, weapons of mass destruction and political turmoil in the Islamic world are lost on many Europeans. For France, Germany and many other Western European states, terrorism is a crime more than an act of war, and stability in the Islamic world is to be found in nuanced diplomacy and support for the current crop of Arab governments, despite their repressive nature. Saddam Hussein's regime was to be contained, not removed from power.

Many Europeans fear that if they take an active role in realising the Bush Doctrine's prescription to bolster democracy in the Middle East, they will become more frequent targets for terrorists, their carefully cultivated relations with Islamic leaders will degenerate and their economic interests and strategies will be placed at risk. Nevertheless, Europeans are beginning to understand that policies aimed at maintaining stability by supporting authoritarian leaders in the region have essentially collapsed. Certainly, they have not been spared inclusion on Osama bin Laden's "enemies' list".

The future of the transatlantic strategic partnership is an open question. In broad terms, and even after the war in Iraq, many Europeans still inhabit a "pre-9/11" and "pre-Bush Doctrine" world. They trust that international institutions or legal arrangements can sustain a peaceful, prosperous and liberal world - a view that was until recently also widespread among Americans. And they remain reluctant to use military force, particularly in pursuit of expansive goals like those now being pursued by the United States in the Middle East.

Yet it is also true that, for the United Kingdom and others, especially the recently oppressed peoples of "new Europe", the United States' new mission is an Atlantic mission. They wish to keep the United States fully engaged in Europe. They are wary of a European Union dominated by France and Germany. And they are increasingly willing to be engaged elsewhere in the world together with the United States. Now enjoying their first taste of the US-led liberal international order, the Pax Americana, they have no interest in creating a European "counterweight".

From a strictly US point of view, even this fractured geopolitical basis is enough to make NATO a useful tool of US statecraft and strategy, as long as the Alliance can reform its military structures to overcome Europe's military weakness.

Although Europe's aggregate economy rivals that of the United States, European spending on military power is less than half that of the United States. Moreover, though that amount is still a lot of money – approximately 140 billion Euros – it buys little of value to the new power-projection missions of greatest interest to the United States. Nor has there been any organised effort to transform European militaries for these new missions or to exploit the technologies that are at the heart of the revolution in military affairs. "Mighty Europe", observed Lord Robertson, "remains a military pygmy."

In combination, these many smaller relative weaknesses combine to create an enormous gap in capabilities between US forces and even the most modern other NATO forces. This is a problem that has its roots in the very structure of the Alliance, in NATO's military response to the Cold War and the threat of Soviet invasion of Western Europe. Put simply, for the United States and, to a lesser extent, the United Kingdom, NATO was a power-projection mission, while for continental Europe and Germany in particular, it was an issue of homeland defence. The military requirement for the United States was to defend West Germany at its eastern border, 3,500 miles from Washington, to deploy "10 divisions in 10 days" and defend the north Atlantic sea lines of communication – even while responding globally to other Soviet probes. The military requirement for West Germany was to defend West Germany.

This inherent structural problem was exacerbated during the late 1970s and early 1980s, when the Reagan Administration began to implement plans for a serious conventional defence of NATO and to rely less on nuclear deterrence. The Reagan build-up, designed not only to fight a strictly defensive war but also to project naval power directly against the Soviet Union and to develop air and land forces capable of counter-attacking deep into Warsaw Pact territory, created not only a "strategic capabilities gap" between US and other NATO forces but also a "tactical and operational capabilities gap". The military history of the past decade – from the first Gulf War through the Balkan interventions and Afghanistan to Operation Iraqi Freedom – is in part the story of how great these gaps have become.

The geopolitical differences and the wide and widening gap in military capabilities between NATO forces have created an undeniable crack in the core of what was, through five decades of Cold War, a central pillar of US national security strategy. Lord Robertson, who admits to being a "paid optimist and an advocate for NATO", argued in February that the Iraq war was not "a make-or-break crisis" for the Alliance, rightly recalling the past debates over "Suez, Vietnam, the INF deployments or the early days of Bosnia". But the question is now fundamentally different. What possible role can NATO play in addressing what President Bush has defined as America's new strategic priority: the roll-back of radical Islam?

Of late, some analysts have described the Alliance disparagingly as a "talking shop". Ironically, in an era of great geopolitical uncertainty and disagreement, there has never been a greater need for a transatlantic talking shop. If France and Germany are to accept the worldview of the Bush Doctrine; if there is to be a positive role in international security affairs for the European Union; if the newly liberated states of Central and Eastern Europe are to be integrated permanently into the West; and if the Atlantic community is to be seen as a set of principles rather than a finite geographic area, then there are profound reasons to continue talking.

Second, NATO must continue to reform its bureaucratic processes. The structures that served the Alliance well in the past are now liabilities to change. Achieving consensus within an expanding coalition in particular is proving extremely difficult.

Third, the primary purpose of bureaucratic reform should be to ensure that NATO maintains its role as a "force provider". As the US armed services have their primary mission to provide trained and ready forces to US commanders, and now US Joint Forces Command has the responsibility to ensure that soldiers, sailors, airmen and marines are competent to conduct multi-service joint operations, NATO will be the principle vehicle through which Americans learn the evolving craft of combined or coalition warfare and stability operations.

Fourth, and intimately tied to its continuing relevance as a force provider, NATO must be the agent for defence reform in Europe. The process of military transformation promises to make the capabilities gap between US (and UK) forces on the one hand, and even the very modern militaries of France and Germany, on the other, all but unbridgeable. New information technologies, in particular, are creating new concepts of military operations and demanding novel organisations. The simple fact is that, as demonstrated in Operation Desert Storm, the Balkans and Afghanistan, and as a matter of strict combat capacity, the United States finds it easier to act unilaterally when the missions are more challenging.

Fifth, NATO must realign itself by shifting to the south and to the east in a strategic movement to connect with the security problems of the Middle East. Forces must be based in new locations. Training must be done in new ways and in new venues. Exercises must be conducted with new partners. And symbolically but importantly, NATO would do well to move its headquarters from Brussels, possibly by expanding the Alliance's Southern Command in Naples, Italy, or by relocating entirely, perhaps to Istanbul, Turkey.

These proposals are not meant to be exhaustive or comprehensive. Though they are ambitious, they are hardly beyond the scope of what is possible for the Alliance. Indeed, the post-Cold-War years have already seen a remarkable transformation. The narrow understanding of the Alliance as an anti-Soviet coalition has been confounded repeatedly. Many analysts warned of the dangers of including a reunified Germany and then expanding NATO to include former members of the Warsaw Pact because of the potential impact on relations with Russia. Now former Soviet republics have been invited to join the Alliance. The NATO-Russia Council brings Moscow itself into the inner chambers of Western security policy-making. And, if anything, the relationship with Russia will prove an additional force for European engagement in stabilising the Islamic world, where Russia has legitimate security concerns.

Some in Europe think that a "small" NATO - not small in size but in ambition - is all the Alliance is capable of. This is a vision of an organisation devoted entirely to providing security within Europe. But beyond the Balkans and a few other modest scenarios, this is a recipe for continued military decline. There is no reason for any member state to build a modern or transformed force to carry out such missions.

At the other end of the ambition spectrum, other analysts think the only way to keep the Alliance alive and vital is to embrace the new missions in the Middle East and elsewhere without reservation. "NATO must go out of area or it will go out of business," it has often been said, meaning that the only validation of the Alliance is by a full, "Article 5" embrace of the US project to reshape the politics of the Islamic world. But with deep geopolitical divisions among major Alliance members, this is a recipe for ever greater confrontation over policy, further restricting the ability of the United States and its willing European partners to act in crises.

The utility of NATO as a war-fighting alliance will be further diminished as it expands. Larger coalitions are always more cumbersome when it comes to making decisions in wartime. Therefore, even as NATO struggles to reshape its decision-making processes to make it a more nimble coalition capable of tackling the security challenges of our time, its immediate military future is in its role as a force provider. This is a fundamental change in how the United States and other members view NATO. The Alliance's "Atlantic community" is now not one defined by geographic boundaries but by the propensity to structure, train and equip forces capable of interoperability with US forces and a willingness to join an institutional "coalition of the willing".