ASHINGTON, Nov. 20 ?The seven-week military campaign in Afghanistan has given the world a stark view of a new American doctrine to make war on the sources of terrorism in the world. But with the defeat of the Taliban perhaps only days away and the hunt for Osama bin Laden intensifying, the force of the American destruction of Afghan targets has sent an unambiguous warning far beyond the war theater to a number of nations that continue to provide bases and training to terrorist groups. The warning is: this could happen to you.

Yet how President Bush takes the war campaign from phase one in Afghanistan to phase two against Al Qaeda and other "global reach" terrorist groups in dozens of other countries remains an unsettled and, in some quarters, an unsettling question.

Deep reservations exist among allies in Europe, the Middle East and Russia over the advocacy by some Bush administration officials who want to expand military operations to other countries, especially by taking the next phase of the war to Iraq to topple Saddam Hussein once and for all.

Although Mr. Bush has yet to speak to the American people about the next phase of the war, its risk and its burdens ?all of which are still under intense debate inside the administration ?the pulverizing effect of the first phase in Afghanistan sends a clear message that the Bush administration has discarded the old military doctrines that applied so rigidly under his father.

At the time of the first Bush presidency, Colin L. Powell, then chairman of the Joint Chiefs of Staff and now secretary of state, prevailed with the Powell Doctrine that "overwhelming force" needed to be massed to defeat an entrenched Iraqi enemy in Kuwait. The doctrine insisted on clear objectives and a clear exit strategy. It now seems possible that such a strategy could have been employed in Afghanistan by massing forces within a coalition to break the Taliban's entrenched conventional forces.

But the second Bush administration has modified that equation in favor of innovative tactics that quickly exploit enemy weaknesses with ruthless bombardment from the air under a doctrine in which the use of force is unrestrained by borders or allies.

Where Mr. Bush now takes this doctrine is an open question, but he has painted his mission broadly across the world.

In his Sept. 20 address to Congress, Mr. Bush put it this way: "From this day forward, any nation that continues to harbor or support terrorism will be regarded by the United States as a hostile regime." He added that while the war on terror began with Al Qaeda, it did not end there. "It will not end," he said, "until every terrorist group of global reach has been found, stopped and defeated."

One great task of wartime leadership, said Eliot A. Cohen, a professor of strategic studies at Johns Hopkins University, "is not only to communicate resolve and determination and will, but to explain what you are doing and why you are doing it."

"I think thus far that is not quite what we have seen," he said. "We have seen a tremendous pulse of staunchness, but we have not seen the more intellectual side of war leadership, making the case for what we are doing and laying out the arguments for what we do next."

To Iraq, Iran, Yemen, Somalia, Syria, Libya, Sudan, and Yasir Arafat's Palestinian Authority, the United States military has demonstrated, as it did in the Persian Gulf war in 1991, the shattering effects of 500- pound bombs dropped on troop concentrations. Once Special Forces spotters got on the ground, American commanders showed how a large arsenal of precision guided weapons could lay the Taliban forces naked to the Navy's carrier-based bombers.

Deputy Secretary of Defense Paul D. Wolfowitz, an advocate of taking the antiterror campaign into Iraq, told an interviewer over the weekend, "I think any government that supports or harbors terrorists should be very worried right now."

Bush administration officials have begun to try to exploit the psychological advantage that is accruing from the fact that they appear to be winning in Afghanistan.

During the weekend, Condoleezza Rice, the president's national security adviser, signaled that Iraq's leader should not be indifferent to what was happening in Afghanistan, if only because the United States had once again demonstrated a level of resolve that might have been underestimated in the region.

"We have said for a number of years that Iraq is a threat to its neighbors, to its people, to the region and to American interests," Ms. Rice said in an interview on CNN. "We didn't need Sept. 11 to tell us that he is a threat to our interests," she said, adding, "We'll deal with that situation eventually."

Even if the goals are more modest than toppling Mr. Hussein, the Iraqi leader will have to consider how much the United States has been changed by the events of Sept. 11, especially in its willingness to support a president who has yet to map out precisely where he is going with his campaign.

Still, what is remarkable just two months into this war is how close the Bush administration has come to its objective of destroying Al Qaeda's sanctuary, how unrestrained the executive power of the president has suddenly become at a time when no war has been officially declared ?and how murky the way forward in this war remains.