ASHINGTON, Sept. 14 ?The last time leaders named Bush, Cheney and Powell faced foreign aggression, their challenge was to marshal a skeptical public, a divided Congress and a reluctant alliance to fight the Persian Gulf war against a known foe on clear turf. Now a new President Bush ?and a Dick Cheney and a Colin L. Powell indelibly shaped by that experience a decade ago ?confront almost the opposite task.

They face an aroused public, a unified Congress and an international alliance that is eager to help ?at least on the surface. But they must find ways to buy enough time and patience to conduct a new kind of long, 21st-century twilight struggle against a shadowy enemy ?or many enemies ?in unknown corners around the world.

"Let me tell you, the only way we can do this and keep the support of NATO is to clearly identify the tentacles, and then the octopus, and then the ink-squirter itself, and then gather it all together and say, `Here they are, and are you ready for what will really be a total military assault,' " said former Senator Alan K. Simpson of Wyoming. "At that point, we have to be so sure."

Or as a former national security official from the Clinton years put it: "The hardest part of this is going to be to convince people to shut up and be patient."

Early polls suggest that Americans believe the terrorist attacks in New York and Washington will result in war, and that sizable majorities would support retaliation, even if innocent people were killed. The realities and complexities of any actual response seem all but certain to affect that support, whether the public winds up confronting American casualties in Afghanistan or civilian deaths elsewhere.

Vice President Cheney, a former secretary of defense, and Secretary of State Powell, a former chairman of the Joint Chiefs of Staff, are patient and methodical men. They know the uses of military force, but, more important, its limitations. They are engaged in planning a global military campaign, not a quick strike or a brief battle. They are thinking in terms of years, not weeks.

And while they balked at marching on Baghdad or toppling Saddam Hussein at the end of the Persian Gulf war in 1991, they are now talking about "ending states who sponsor terrorism." Having witnessed the fall of the Soviet Union, they are fully aware of how cataclysmic such a change could be.

"This operation isn't going to be quick, or pretty, or certain," said Anthony H. Cordesman, a senior fellow at the Center for Strategic and International Studies in Washington. "To do anything at all is to invite an element of ambiguity. There's going to be casualties and collateral damage. That's why we call it war."

All week, senior administration officials have made it clear that they would not settle for largely symbolic strikes against suspected terrorist training camps or against a target identified as a military factory, the way the Clinton administration did after attacks on United States embassies in Kenya and Tanzania.

"I was raised a soldier," Secretary Powell said at his briefing today. "And you're trained there is the enemy occupying a piece of ground. We can define it in time, space and other dimensions, and you can assemble forces and go after it.

"This is different. The enemy is in many places. The enemy is not looking to be found. The enemy is hidden. The enemy is, very often, right here within our own country. And so you have to design a campaign plan that goes after that kind of enemy, and it isn't always blunt-force military, although that is certainly an option. It may well be that the diplomatic efforts, political efforts, legal, financial, other efforts, may be just as effective against that kind of an enemy as would military force be."

The deputy secretary of defense, Paul D. Wolfowitz, made a similar point on Thursday when he said, "I think everyone understands that we have, unfortunately, entered a new era," as he outlined the administration's commitment to "removing the sanctuaries, removing the support systems, ending states who sponsor terrorism." It was Mr. Wolfowitz, as a top Pentagon official under Mr. Cheney, who devised the elder Bush administration's plan to solicit contributions from an alliance to help finance the Persian Gulf war.

In his homily at a prayer service at the Washington National Cathedral this morning, President Bush described the mission in even grander terms, saying: "Just three days removed from these events, Americans do not yet have the distance of history, but our responsibility to history is already clear: To answer these attacks and rid the world of evil."

That makes Woodrow Wilson's pledge to make the "world safe for democracy" sound simple by comparison.

Former President George Bush said Thursday: "It is far more difficult to fight an enemy who refuses to show his face."

The former senior national security official who asked not to be identified said there would be nothing easy about the task ahead. "There'll be the amount of resources we put into domestic surveillance, balancing that with civil liberties," the official said. "And then abroad, if we are talking about bin Laden, we're talking about a network that operates in different places. The United States, with our allies, has taken down a lot of these cells in the last two years, many more than people know. Finally, if there is a military component, we will have to define the objective in an achievable way."

If, as the weeks wear on, Saddam Hussein is shown to have had any hand in fostering the attacks, or exploits them for the instability they create in the Middle East, questions will doubtless resurface about why the first Bush administration, led by so many of the same people now in positions of power, did not press on to invade Iraq.

Besides Mr. Cheney, Mr. Powell and Mr. Wolfowitz, other veterans of the gulf war have roles in this administration, including Condoleezza Rice, then a Soviet expert on the National Security Council staff and now its head, and Richard N. Haass, then the Middle East expert at the N.S.C. and now director of the policy planning staff at the State Department.

The current President Bush, whose recent preoccupations have been the budget and taxes and fears of a faltering national economy, must also be all too aware, given his father's own example, how much those problems could still affect his fortunes, whatever his foreign policy successes or failures. Indeed, some of the biggest challenges may turn out to be at home.

"The challenge is to take all the pollsters and all the consultants and put that all aside," said former Senator Bob Kerrey of Nebraska, who now heads the New School University in New York. "This is the wealthiest nation on earth, and please don't tell me that you can't put enough money out there to make certain that men with hand knives and box cutters can't hijack four American planes within an hour. Now we know that every airplane that takes off in America is a bomb, fully loaded. So deal with it. Don't let the lockbox or ideology or anything else get in the way of that."

Mr. Kerrey, a combat veteran of Vietnam, also pointed out the psychological challenge for leaders and a public that have been quick to denounce the attacks as the work of cowards or madmen.

"I condemn it morally, and I do think it was cowardly," Mr. Kerrey said. "But physically, it was the opposite of cowardly, and if you don't understand that, then you don't understand the intensity of the cause and then you're papering over one of the most important things. There is hatred out there against the United States, and yes, we have to deal with terrorism in a zero-tolerance fashion. But there is anger, too, and they ought to have a place for a hearing on that anger, in the International Court or wherever we give them a hearing."