While at least 38 Marine and Army troops have died in a tough week of house-to-house fighting in Fallujah, that is not the hardest part of the U.S. counteroffensive against the Iraqi insurgency.

The U.S. strategy in Iraq, Marine Col. T.X. Hammes observed in a recent interview, is a three-step process. "Clear out the insurgents, build up the Iraqi security forces, and then develop and install local governments in preparation for national elections," said Hammes, who served in the U.S. occupation authority in Iraq last winter.

The second and third steps promise to be more difficult to take than the first, in part because they are largely beyond U.S. control. Yet those steps of "Iraqifying" security and politics are also the keys to the Bush administration's strategy for getting out of Iraq. And over the course of the 18 month-long insurgency, U.S. officials frequently have overestimated their progress, both in creating durable Iraqi police and military units and in laying the groundwork for Iraqi political control of the country.

On top of that, even the initial step of clearing out the insurgents is hardly concluded. While major fighting appears to be ending in the western Iraqi city of Fallujah, U.S. officers say they expect combat to roil central Iraq in the coming days as they try to exploit their gains. They think they have the insurgents on the run, but other experts warn that the anti-U.S. forces also may be growing stronger in that part of the country.

"The next 10 days are a crucial period," a senior U.S. military officer, who spends extensive amounts of time in Iraq, said in a telephone interview yesterday. "My intention right now is to keep the pressure on, not let them go to ground, but batter them for the next 10 days to two weeks," said the officer, whose position does not allow him to be quoted by name.

He said captives are giving up a trove of intelligence, from "pocket litter" to travel documents to laptop computers, that will be exploited with a series of actions across central Iraq's Sunni Triangle, from Fallujah to Baghdad to Samarra and Tikrit. Most leaders of the insurgency left Fallujah before the U.S. offensive began, but have not gone far, this officer said, either to Baghdad or the northern part of Babil province.

Meanwhile, he said, reconstruction will begin in Fallujah to signal that Sunnis are still desired as part of the political process, a key point to make as nationwide elections are scheduled for January. The bridge to that vote, which the United States believes is crucial to undercutting the insurgents, will be getting Iraqi allies of the U.S.-led occupation to replace U.S. forces and assert themselves in such a way as they have not yet shown they can do.

"The key will be if government forces can hold Fallujah, Mosul, et cetera, after they are taken or stabilized, and, more importantly, if the Iraqi government can convince the bulk of the Sunni population that their lot is better off with the new Iraq," said Michael Vickers, a former CIA officer who is a Pentagon consultant.

There are two major variables in the current equation in Iraq, and neither one is American in nature. One is the health of Iraqi security forces. The other is the strength of the anti-American insurgency.

There is general agreement that Iraqi soldiers are performing markedly better now than they did in the spring, when some Iraqi police fired on U.S. troops and an entire battalion refused to go to Fallujah to help U.S. forces. "They certainly did better than they did in April," said one Army officer who has served in Iraq. "They showed up."

Hammes, who recently wrote a book on insurgency titled, "The Sling and the Stone: On War in the 21st Century," agreed, saying that while some Iraqi troops deserted, "The real story here is that many Iraqis stayed and fought. They are the nucleus from which we will grow a genuine army."

But others are skeptical that much progress has been made. Jeffrey White, a former Defense Intelligence Agency analyst who is at the Washington Institute for Near East Policy, said he saw little evidence that Iraqi forces were capable of doing much on their own. "Based on their casualties in Fallujah -- six KIA -- and eyewitness accounts, it looks like the Iraqis were not asked to do much, if any, serious fighting," he said.

The other half of the equation is the strength of the insurgency. U.S. officers, impressed by the 1,000 insurgents they believe have been killed in Fallujah, with an additional 1,100 taken captive, believe they have dealt a heavy blow to the rebels. They suspect that the spate of attacks from Baghdad north to Mosul has been a "media play" by a staggering insurgency to give the impression that it has not suffered a major defeat in Fallujah.

But some other experts think the insurgency is more robust than that.

Maj. Adam Strickland, a Marine specializing in insurgency issues, said that speaking for himself and not for the Corps, he thinks the anti-U.S. fighters are hardly on the run. "This was simply the insurgents testing our resolve and strength, as well as their own," he said. "They will simply fall back a phase in the classic Maoist struggle."

White, whose analyses over the last 18 months generally have been far more prescient in discerning trends than official U.S. government pronouncements, said he worries that the insurgency is showing new capabilities, with better command and control across the Sunni part of the country. "What we are seeing is organized, regionwide resistance," he said. "The resistance is fighting harder, smarter and more effectively than the Iraqi military did during the war."

One expert who has served in Iraq, in the Army and in the private sector, said he worries that if that is the case, the coming months will bring several more Fallujah-like fights. "It has evolved into one big vendetta -- a blood feud between us and the Sunnis," he said, speaking anonymously because his company would not allow him to be quoted by name.

Likewise, a security consultant in a similar position in Baghdad said that in his view, the insurgency is becoming increasingly tough, in part because it is gaining more popular support.

"We are without allies amongst the Iraqi populace, including those who have benefited from the ouster of Saddam," said this Special Forces veteran, who speaks Arabic. "Across Baghdad, Latifiyah, Mahmudiyah, Salman Pak, Baqubah, Balad, Taji, Baiji, Ramadi and just about everywhere else you can name, the people absolutely hate us. . . . The Iraqi people have not bought into what the Americans are selling, and no amount of military activity is going to change this fact."

He argued that the United States should simply freeze all attempts at reconstruction at this point and send the contractors home, telling the Iraqi people, "Call us when you want help."