The rapid advance of the Army's 3rd Infantry Division and the 1st Marine Expeditionary Force to the outskirts of Baghdad yesterday presents Army Gen. Tommy R. Franks and his subordinate commanders with the biggest battlefield dilemma they have faced in the two-week-long Iraq war: whether to assault the capital now or to wait two weeks or more for reinforcements.

Part of the answer will turn on their assessment of the fragility of the government of Iraqi President Saddam Hussein. Another factor will be whether their intelligence analysts believe that Hussein's most loyal fighters, drawn from the Republican Guard and his bodyguard Special Republican Guard, have concluded that the only effective way to counter the U.S. attack is by holing up in the city and waging a grinding war of attrition. That would follow a strategy that Hussein loyalists have used with some success in southern Iraqi cities.

Also, the Iraqis know that with a U.S. approach designed to end the war as quickly as possible, the U.S. military is unlikely to follow the example of the British forces outside Basra and sit at the city limits, refusing to take the bait.

Essentially, Franks has to decide whether to wait for the tank-heavy 4th Infantry Division, which defense officials say won't be ready to join the attack until the middle of the month.

The force Franks and his commanders ultimately will confront is certainly smaller than it appeared to be before yesterday. At least two of the three Republican Guard divisions south of Baghdad no longer appear to be effective military units, defense officials said. Two weeks of intense aerial bombardment, coupled with artillery barrages and multiple-launch rocket fire, apparently devastated the Guard positions around the cities of Karbala, Hilla and Kut.

Pentagon officials said stragglers have no doubt fallen back into Baghdad and may try to hook up with Special Republican Guard units and members of Saddam's Fedayeen, a Baath Party paramilitary force that has waged guerrilla-style attacks on U.S. and British troops in southern Iraq. Also, some of the Republican Guard units still stationed north of the capital may try to move southward, but U.S. officials are confident of their ability to attack them when they move. Finally, Pentagon officials said, allied troops will no doubt face small ambushes on their way in to the city from snipers and hidden tanks.

But, Pentagon officials said, any organized retreat by the Republican Guard into the capital has been thwarted. Optimists said the Guard simply was wiped out. Even pessimists said that what is left of the Guard -- which before the war was estimated to number 60,000 troops -- is demoralized, running out of food and water, and cut off from its supply lines.

The path to Baghdad is "wide open," one defense official said.

But on the other side of the Pentagon, another official rejected the notion of a hasty assault on the capital. "I don't think we're going to rush right in there," he said. He said the likely next step is to surround the city, secure U.S. supply lines that were lengthened by yesterday's gallop northward and eventually demand an unconditional surrender. Some officials predicted that the Army and Marines would spend a week or two making sure that the three Republican Guard divisions deployed on the southern side of the capital are wiped out.

"I sure as hell would want" the 4th Infantry Division before attacking Baghdad, said retired Army Col. W. Patrick Lang, a former expert on the Iraqi military for the Defense Intelligence Agency. "We're going to need a bigger force for this."

He and others predicted that U.S. forces would conduct some probes into the capital to retain the military initiative, test the city's defenses and keep the Iraqi government off balance. But they predicted U.S. commanders would not launch the assault on Baghdad until they have concluded they would no longer face resistance from Republican Guard divisions south of the capital and until reinforcements have arrived.

If an American unit gets into an unexpectedly tough fight, Lang warned, "There's not a whole lot behind them" to help them out.

Not all experts agreed that U.S. forces should proceed with caution.

Retired Marine Col. Gary Anderson, an expert in urban warfare who has participated in several war games of an Iraq invasion, predicted that U.S. commanders would take a gamble and immediately test the defenses of the capital to see if a sharp rap would shatter the government.

That approach would be in keeping with a war plan that already has rolled the dice more than is customary in the U.S. military, such as launching a ground offensive without a preparatory bombing, and then racing across southern Iraq without troops to secure a 250-mile-long supply line.

"My feeling is that once the outer ring is cracked, the regime will go fairly fast," Anderson said. "Give it a try, and fall back to Plan B if you have to."

The hazard of that approach is that probes sometimes turn into big battles. And if the U.S. military gets into a fight without adequate forces on hand, it will revive the debate over the war plan that turns on the question of whether Defense Secretary Donald H. Rumsfeld and other civilian leaders pushed the military into invading Iraq with a force too small, especially on heavy armored units. Rumsfeld and the chairman of the Joint Chiefs of Staff, Air Force Gen. Richard B. Myers, vigorously rejected that view at a news conference Tuesday at the Pentagon.

In a war whose rhythms have been erratic, the unpredictability of the situation seemed to be peaking yesterday. "We're approaching the time of desperate measures, of the maximum risk of chemical weapons, or of a political coup," said Jeffrey White, another former DIA expert on the Iraqi military.

He doesn't expect chemicals to be used by Iraqi defenders because, he said, the tactical advantages on the battlefield wouldn't be great but the strategic costs to Hussein's image would be. U.S. commanders have worried that the most likely time that chemicals would be used was as U.S. forces crossed the "red line" demarcating the defensive perimeter of the capital, a boundary they crossed yesterday.

If a coup is going to be launched against Hussein, White added, this would be the time. The key factor at this point is whether the apparent destruction of two Republican Guard divisions yesterday has a discernible effect on the stability of the Iraqi government, he said.