The Army brigade that has served the most time on the battlefield since 2001 is coming home. But as they return, troops may have to leave two of their own behind in Iraq.

Members of the 2nd Brigade, 10th Mountain Division are searching up to the last minute, trying to find two fellow soldiers captured by insurgents and missing since May.

"This is still our brigade's No. 1 priority," its commander, Col. Michael Kershaw, said Friday.

"We've been doing everything possible to bring them back before we leave," he told Pentagon reporters via videoconference from Iraq.

Spec. Alex R. Jimenez, 25, of Lawrence, Mass., and Pvt. Byron W. Fouty, 19 of Waterford, Mich., were seized May 12 when hostile forces attacked and overran a checkpoint during an operation to watch for insurgents placing roadside bombs on a dangerous road south of Baghdad.

They are two of more than 300 casualties suffered in Iraq by the brigade from Ft. Drum in northern New York state.

Casualties taken by the 3,600-member brigade have totaled 52 killed and more than 270 wounded in action, Kershaw said.

The brigade is in its 14th month of an extended 15-month tour — "The most-deployed brigade in the U.S. Army," he said. On its return home, expected to be completed over the next several weeks, it will have served overseas 40 months since December 2001.

The brigade has served two tours in Iraq and elements of it have served twice in Afghanistan, according to Army records.

Four U.S. soldiers and an Iraqi translator were killed in the May ambush some 20 miles south of Baghdad in which Jimenez and Fouty were taken.

Their identification cards were later found in an Al Qaeda safe house north of Baghdad, along with video production equipment, computers and weapons. The house was more than 100 miles from the area where they disappeared.

The Islamic State of Iraq, an Al Qaeda front group, claimed in a video posted on the Internet the soldiers were killed and buried.

Asked Friday if he believe they were still alive, Kershaw said captured suspects and "numerous other intelligence sources ... have given us really all different kinds of stories."

"Just last week we received one significant intelligence thread that indicated that they at least were potentially alive recently, but another that said that that they had been killed shortly after the attack," Kershaw said.

The attack triggered a massive search in an area that is part of the "triangle of death," named for the rampant insurgent activity there. U.S. aircraft dropped leaflets seeking information; U.S. and Iraq forces searched muddy canal areas, farmlands and fields.

"We flooded the area for about six weeks in a detailed search," Kershaw recalled Friday, "and continued a more surgical search since then." A dozen insurgents involved in the planning and execution have been captured and other suspects may have been hit in a strike just Thursday night, he said.

He didn't identify any of those involved except to say the attackers were 15 to 18 people affiliated with Al Qaeda.

Jimenez's wife Yaderlin Hiraldo Jimenez — an illegal immigrant — was threatened with deportation but later given a green card out of respect for her husband's sacrifice, U.S. government officials said.

The 2nd Brigade will be replaced in Iraq by the 3rd Brigade, 101st Airborne Division. In the transition over the coming weeks, they will be briefed on lessons learned by Kershaw's brigade over the last 14 months.

"One of the primary responsibilities that we'll talk about is the continuing search for our missing soldiers," so the new troops can carry on the effort, he said.

Kershaw said there has been great progress in his sector during his brigade's time there. Thousands of Iraqis have allied themselves with the coalition and have applied to join the Iraqi police. Economic conditions are improving and children who had been working on farms are starting to go to school, he said.

"You can rest assured that although we've had some heavy sacrifices, our contributions have been significant," Kershaw said. "And we're going to leave south Baghdad better than we found it."