WASHINGTON - One week after the Iraq war started with a U.S. bomb and missile strike aimed at Iraqi leader Saddam Hussein and his top generals, the American-led campaign is proceeding at a blistering pace and with notable achievements: Much of southern Iraq has fallen to allied forces, the southern oil fields are secure and troops are nearing Baghdad, with relatively little loss of life to either combatants or civilians, say Pentagon officials and analysts.

But the most difficult part of the war might be coming in the next several days. The Army's 3rd Infantry Division and the 1st Marine Expeditionary Force are storming northward to attack Hussein's elite Republican Guard divisions and decide how - and whether - to enter Baghdad to complete the mission of toppling the Iraqi leader.

And with that come the nightmare scenarios, from poisonous chemical and biological clouds, to stiff resistance from well-trained Republican Guard divisions, to street-to-street fighting that could grind up American forces and lead to untold civilian casualties, all caught live on worldwide television.

"The advance of the 3rd Infantry is nothing more than astonishing," said Andrew Krepinevich, a retired Army colonel and an analyst with the Center for Strategic and Budgetary Assessments. In less than a week, "they have gotten to the outskirts of Baghdad."

Michael O'Hanlon, a defense analyst with the Brookings Institution, agreed but was more cautious: "The real fight's still ahead with the Republican Guard."

Reviewing the first week of the war, it seems clear that the Pentagon was overly confident about the effect of the initial air bombardment that it said would bring "shock and awe" to Hussein and senior members of his regime. And military planners believed that the southern part of the country, dominated by Shiites who despise Hussein, would fall quickly to advancing forces. Much of it has, but there are still pitched battles under way in some sectors.

Three weeks ago, Gen. Richard B. Myers, chairman of the Joint Chiefs of Staff, told reporters that the Iraqi leadership would be on the receiving end of an unprecedented and overwhelming bombing campaign with precision weaponry. He predicted "such a shock on the system that the Iraqi regime would have to assume early on the end was inevitable."

But Loren Thompson, a defense analyst at the Lexington Institute, said, "I don't think the air attacks were sufficient." Hussein and his chief lieutenants appear to be alive and well, relaxed and smiling at meetings broadcast on Baghdad television, while Republican Guard units are gearing up for a fight.

The Republican Guard units "haven't been under heavy attack for long," said Thompson, adding that bombers and attack aircraft should have been used to a greater extent, rather than relying on Apache attack helicopters, as has been the case in recent days.

Retired Army Gen. Barry McCaffrey complained that the 3rd Infantry Division failed to bring adequate numbers of artillery batteries that could have helped deal with the Iraqi threat to the heavily armed helicopters. "When the Apaches went up, they all got shot full of holes," McCaffrey said. "We suppress enemy fire with artillery."

At the same time, the military planners seemingly failed to appreciate the strength of Hussein's paramilitary units, the fedayeen, who are dressed as civilians and seeded throughout the cities of the south, skirmishing with U.S. and British forces, killing and capturing soldiers and striking at the lightly defended and lengthy supply line that extends about 250 miles from the Kuwaiti border to coalition positions outside Baghdad.

Hundreds of these highly trained irregulars, who publicly pledge their lives to Hussein, are holding hostage the populations of An Nasiriyah and Basra, the country's second-largest city with more than 1 million people, according to the Pentagon.

Both British Royal Marines in Basra and U.S. Marines in Nasiriyah are mounting raids through both cities, killing paramilitary units and members of Hussein's Baath party.

Pentagon officials bristle at suggestions that these irregular Iraqi forces surprised them, although a British spokesman seemed to confirm that to reporters yesterday. "The irregular elements have been greater than predicted and their resolve has been greater than expected," said British Army Col. Chris Vernon, a spokesman for United Kingdom land forces.

Current and retired U.S. Army officers are complaining that the long supply line between Kuwait and coalition forces approaching Baghdad is stretched thin and too lightly defended. Two dozen soldiers from an Army maintenance unit were attacked by irregulars; seven Americans were killed and five were taken prisoner.

Yesterday, Myers and Defense Secretary Donald H. Rumsfeld denied that there was a security problem on the supply lines, with the defense secretary dismissing attacks by the irregulars as "ones and twos, that you're going to live with, like you live with in Afghanistan."

One defense official said that there are no plans to provide additional forces to protect supply lines and provide convoy security. "I don't think we're beefing anything up," he said.

But Vernon, the British Army spokesman, estimated there are 1,000 fedayeen in Basra alone and supply lines were being augmented with "more rear security" forces.

Moreover, the New York Times reported today that the battle for Baghdad might be delayed so the fedayeen and other irregular units can be neutralized and the bitterly contested southern areas pacified.