The immediategoals of the militarycampaign against Afghanistan enjoy broad international support. The air strikes seek to clear the way for other military efforts to destroy al-Qaeda's terrorist network in Afghanistan, capture or kill Osama bin Laden and his lieutenants, undermine the Taliban's rule and deliver humanitarian assistance to the Afghan people - all in an effort to ensure that Afghanistan can never again be used as a base for terrorist operations.
But make no mistake, there is a larger objective behind the military operations in Afghanistan: that of sending a message to terrorist groups and the states that sponsor them that they will pay dearly for engaging in and supporting terrorism.
For Washington, Afghanistan is only the first phase of a long anti-terrorist campaign. In an address to Congress, George W. Bush was explicit: "Our war on terror begins with al-Qaeda but it does not end there. It will not end until every terrorist group of global reach has been found, stopped and defeated." As for state sponsors of terrorism, Mr Bush warned: "Any nation that continues to harbour or support terrorism will be regarded by the United States as a hostile regime."
More recently, the letter to the United Nations Security Council by John Negroponte, US ambassador to the UN, makes the same point. "We may find that our self-defence requires further actions with respect to other organisations and states."
Much has been made in recent weeks about a supposed rift within the Bush administration about the overarching goal of the anti-terrorist campaign. In the early days, Colin Powell, the secretary of state, and some in the Pentagon led by deputy secretary Paul Wolfo-witz, disagreed over whether to focus initially on Afghanistan or begin with a broader military campaign that included strikes against Iraq and other state sponsors of terrorism. Mr Bush settled on an Afghanistan-first strategy. But it would be a mistake to confuse this with an Afghanistan-only strategy.
Mr Bush's war against terrorism is therefore much broader than simply focusing on Mr bin Laden and the Taliban. It encompasses the al-Qaeda network outside Afghanistan, Hizbollah, Hamas and other groups of "global reach" as well as the states that continue to sponsor them - including possibly Iran, Iraq and Syria. It may even include terrorist groups such as the Real IRA, particularly if they co-operate with terrorists a continent away.
In fighting this broader war, Washington will be making specific demands on the state sponsors of terrorism. They must close down terrorist training camps on their soil or under their control; cease financing terrorist groups and co-operate with international efforts to cut money flows to terrorists; and publicly renounce the use of mass violence deliberately aimed at civilians for political ends.
To persuade terrorist groups and their supporters in Baghdad, Damascus and Teheran to change their ways, the US will pursue a strategy combining vigorous diplomacy, targeted economic sanctions and co- ordinated law enforcement and intelligence operations. But the strategy will ultimately rest on willingness to do elsewhere what the US and its partners are now doing to the Taliban: destroy the ruling regime.
Britain appears to understand what is involved. As Tony Blair told the House of Commons on Monday: "We are in this for the long haul. Even when al-Qaeda is dealt with, the job is not over. The network of international terrorism is not confined to it."
But it is not clear that other members of the international coalition share this view. They seem to believe that the goal should merely be vigorous law enforcement, punishing only those directly responsible for the September 11 attack and their immediate supporters.
Even if most European states would prefer a narrower goal, they have a big role to play in the broader campaign against terrorism. If they wish to reduce the chances of the US and Britain using force elsewhere in the Middle East, they need to exercise their considerable diplomatic, economic and political power to persuade Iraq, Iran and Syria to abandon their support for terrorism. Russia, too, can be particularly helpful, especially with Iran, in persuading its friends to join the fight against terrorism. With the implicit threat to use force against regimes that continue to support terrorism, such actions may eliminate the havens on which terrorists depend.
There are risks in this broader strategy - not least in further alienating moderate Arab and other Muslim countries that for now are grudgingly going along with America's course. And as in the cold war of yesteryear, defeating terrorism with a global reach will take years and much effort to accomplish. The US cannot achieve this goal alone. Washington needs partners. And while not everyone will agree on the appropriate means, all should agree on the appropriate ends.