The captain spotted the two men, in the garb of suicide attackers, sneaking through the culvert, using the dark green water to hide their movements as they edged closer to the American armored vehicles. He tossed grenades at them.

Plumes of water flew up, but the Iraqis still advanced.

They ducked when Capt. Chris Carter grabbed the 12-gauge combat shotgun and fired into the water. But then one stood with his Kalashnikov assault rifle. Carter shot him in the head.

"Kif, kif, kif!" Carter shouted in Arabic at the other. Stop!

He did not. Fifteen feet from Carter's Bradley, he stood with his rocket-propelled grenade launcher, ready to fire. So Carter cut him down.

"That stupid, little ...," Carter said. "He wouldn't give up."

The unit Carter commands -- A Company, 3rd Battalion, 7th Infantry Regiment -- was about five miles south of the Baghdad city limits when they encountered the attackers Sunday. This was a normal patrol; as U.S.-led forces completed the circle around Baghdad, they continued to engage Iraqi fighters in sporadic firefights.

Across the landscape, guerrillas -- hard to pick out from the non-combatants they often hid behind -- sprayed automatic-weapons fire at American troops, courting tragedy.

"There's a guy in white, a lot of darting movement, keeping down real low," an excited Marine told his unit commander over the radio, during a skirmish on the southern outskirts of Baghdad. "Request permission to take a potshot at him."

The radio voice squawked back at him: "Not amused."

"If they have got weapons and they're darting in and out, drill them," his commander answered. "A lot of these people are civilians and you've got to use good judgment."

With U.S. forces hunting down Republican Guard and other forces south of Baghdad, a message read Sunday on Iraqi radio and television in the name of President Saddam Hussein called on any soldiers separated from their original units to join any other unit and rejoin the battle with the Americans. The statement suggested the Iraqis' disarray after days of pounding from the air and U.S. ground assaults.

Marines fought street-to-street battles for control of a bridge over a canal, leading into Baghdad's southeast corner. They won the bridge but could not use it; Iraqi fighters dug out its embankment to weaken the span, and rigged it with explosives. Iraqi soldiers were naked or in their underwear when they were captured, rushing to get into their civilian clothes.

One Marine suffered a minor shrapnel injury. Iraqi casualties were estimated at 30 to 80 dead; at Central Command headquarters in Qatar, a spokesman said enemy casualties were based on estimates by field commanders rather than any precise formula. On Sunday, Central Command said 2,000 to 3,000 Iraqis had been killed in Saturday's Baghdad incursion.

"It's not scientific, especially when you're on the move at 25 mph or 35 mph," Navy Capt. Frank Thorp said.

To the southeast, at the Tigris River town of Salman Pak, U.S. forces searched what was believed to be a terrorist training camp, where they found obstacle courses, storehouses filled with gas masks, and the shell of a passenger jet -- perhaps a teaching aid for hijackers.

They also sifted through the Republican Guard's 2nd Corps Headquarters, coming away with parts of computers and what Lt. Col. Michael Belcher called "critical documents" regarding enemy weapons and communications.

And they got a close-up look at the lives of their adversaries, in what appeared to be part of a junior officers' training camp for the Republican Guard. They saw snapshots of friends and children; a simple gym with pictures of soccer teams on the wall; a mess hall, where the walls were painted with Bedouin scenes, sayings from the Koran and quotes from Saddam.

"Going through this stuff you can tell a lot of them are just ordinary guys," said Gunnery Sgt. Michael Templeton, 39, of Livonia, Calif.

When Carter and A Company got a good look at the two men he killed in the firefight at the culvert, they found proof that they were in no way ordinary.

The bearded men, in their early 20s, had red head bands with "Allah Akbar" written in black marker across the front, the traditional insignia of the suicide fighters, self-described martyrs, who have appeared on Iraqi television pledging to fight the advancing U.S. troops.

They carried six RPG rounds in a white flour sack, one launcher and one assault rifle.

The patrol had begun with a warning, as Iraqi civilians returned to their homes after fierce fighting overnight. Interviewed by a U.S. Army intelligence agent, one man, identified only as Hatif, warned of suicide attackers on the road toward Baghdad.

As the column of 10 Bradley fighting vehicles rolled north through a village, six men dressed in dark, civilian clothes with red-and-white checkered scarves on their heads scrambled into the brush. Within minutes, they fired two rocket-propelled grenades from a tree line near the road, striking the lead Bradley just above the driver's hatch, piercing it and sending a cloud of hot white gas and flecks of shrapnel into the turret and passenger compartment.

"There was a big boom and a white flash that didn't go away, I thought it was a fire," Spc. Kenneth Clark of Woodward, Okla., said. "I felt heat and stinging all around my head and neck."

The men in the Bradley bailed out into a hail of small arms fire, scrambling to take cover by a mud wall. Three were hit by shrapnel, mostly scratches, except for the driver who had a wound near his eye. An armored ambulance, emblazoned with a red cross and nicknamed Dark Angel, raced to the front of the convoy and dropped its rear door. The injured soldiers climbed in.

The infantrymen were navigating narrow roads through small farming villages, traveling without the normal protection of tanks taking the lead, leaving the Bradleys vulnerable to rocket-propelled grenade ambushes.

"They got me again," protested Staff Sgt. Thomas Slago of Los Angeles, commander of the Bradley that was hit. His Bradley had been hit by an RPG in an earlier battle. "I'm tired of being an RPG magnet."

The Bradleys rolled forward near where they had seen the Iraqi fighters run away and soon RPGs were flying again. U.S. troops returned fire, killing two Iraqis.

The Iraqis were using a complex of canals, irrigation ditches and levees for cover. On one levee, they had built a bunker, which 1st Lt. Lars Nadig of Hamilton, Va., the platoon leader, said they were using to get more ammunition.

"I'd like to get my boys on the ground and get these [guys]," Nadig told Carter by radio.

"Then let's get these [guys]" Carter replied.

The back ramp of one of the platoon's Bradleys opened and six men ran out in full combat gear. They dropped behind a berm and took up firing positions, peppering the levee in front of them with bullets from their M16A4 and M4 assault rifles.

Throwing grenades in every culvert, the soldiers worked their way up to the levee, tossing grenades over the side where they had last seen the Iraqis. In the end, they killed them all.

Until now, the troops of A Company, nicknamed Attack, had only seen soldiers and Republican Guard fighters, not suicide attackers. The combat had also never been so close.

"They are hard fighters, but not smart fighters," Carter said.