* Veteran Lakhdar Brahimi, 80, likely on last peace mission
* Proved himself in Lebanon negotiations decades ago
* Opposition delegate says he shows "impeccable neutrality"
By Khaled Yacoub Oweis
GENEVA, Jan 29 (Reuters) - The job was too much for Kofi Annan. The Nobel Peace Prize-winning former U.N. secretary general - hardly known as a quitter - threw in the towel in August 2012, declaring that serving as international mediator for Syria was impossible as long as global powers were hopelessly divided.
Few expected much progress from Annan's replacement. But since taking on the role, Lakhdar Brahimi, an 80-year-old Algerian diplomat with decades of experience in some of the world's most intractable conflicts, has steadfastly refused to give up on what is expected to be his final mission: seeking an end to Syria's civil war.
It took Brahimi a year and a half even to get the warring parties into the same room for this week's peace talks in Geneva. Any peace deal still looks remote at best. He has regularly come under criticism from both sides, most recently from the government which accused the noted secularist of sympathy with Islamic radicals.
Yet despite the seeming hopelessness of his task, his supporters - including a range of diplomats across the Middle East and beyond - say there is no one better suited to try.
"I quite admire him, I must say, for hanging in there and sticking with this impossible mission he has," said Karen Koning AbuZayd, a member of an independent U.N. war crimes inquiry into Syria and a former head of the U.N. agency helping Palestinian refugees known as UNRWA.
"He is an old, old, friend of mine and of some of the others here. He's a very clever man with a lot of experience," she said. "He knows where we come from."
Brahimi himself has been keen not to be tripped up by unrealistic expectations: "These people did not meet once in three years. They did not expect there would be a magic wand to finish the 1,000-mile walk," he told reporters on Wednesday.
"If we walk the first step it will be very good."
Brahimi, who hails from an aristocratic Algerian family, cemented his reputation as a mediator in the role of Arab League envoy during the civil war in Lebanon in the 1980s, becoming one of the few figures to emerge from that drawn-out diplomacy with an enhanced reputation.
After first trying to secure the release of hostages held by Shi'ite groups linked to the Lebanese group Hezbollah, he eventually helped put together the Taif agreement of September 1989 that ultimately ended the 15-year conflict.
The almost impossibly complex agreement set up a system for sectarian communities to divide senior state positions that has held up since, effectively becoming Lebanon's constitution.
It was not without holes: the first president chosen under the agreement was assassinated, and Syrian troops who were expected to withdraw within two years ended up staying for 15. But it remains the gold standard for Middle East diplomacy.
Crucially, that agreement won support not only from the warring parties themselves but from their myriad foreign backers - Western countries, Sunni Muslim Arab states and Shi'ite Iran - the same parties on the sidelines of Syrian talks today, whose agreement then seemed as unlikely as it does now.
Many figures hovering around Geneva now are familiar faces with whom Brahimi has built up decades of trust.
"Brahimi's Middle East experience precedes almost everyone in the region," said a diplomat who has worked with him on other intractable problems. "That gives him a big advantage over anyone else trying to mediate an end of the conflict."
According to people who have been in meetings with him, Brahimi has made it clear that a large part of his work is improvising.
He jokingly told journalists this week he welcomed their ideas on how to bridge the gap on setting up a transitional administration for Syria, the most contentious issue, which the government rejects and the opposition demands.
Asked whether he was likely to follow the model for peace talks between North and South Vietnam in the 1970s, he told reporters: "I don't think we are following any model at all. We are doing what the situation allows, what the market can bear."
He has had to rescue the talks from collapse over issues as lofty as whether Assad must leave power, and as petty as who should sit in the conference room with whom.
The talks took a first tentative step forward on Wednesday as both sides agreed to use the same document as the basis of discussions, although they disagreed about how the negotiations should proceed.
The diplomat who has worked with him before said Brahimi does not intend to let the talks drag on without results: "He realises this is the last mission of his career. He will not hesitate to wrap things up if the talks go nowhere."
If criticism from both sides is a sign of neutrality, Brahimi has demonstrated it. Initially he drew more fire from the opposition, visiting Damascus several times to meet President Bashar al-Assad and proposing talks at a time when the opposition said it would not meet unless Assad left power.
Sources inside the peace talks have described tough exchanges this week with the government delegation. With typical tact, Brahami brushed off suggestions of a quarrel.
Ibrahim Jaafari, a senior negotiator in the Assad government team, attacked Islamist ideology at Monday's meeting, the sources said. Brahimi tried to stop him by saying that the United Nations was not the place for such words.
Jaafari replied that Brahimi was just a mediator and could not speak in the name of the world body. At one point he told Brahimi: "You can become a Wahhabist if you want," referring to a strict school of Sunni Islam.
Brahimi told reporters later that the incident was exaggerated: "If ... somebody said the government side had said horrible things about religion, and I scolded them, it is not true. I don't scold anybody, to begin with," he said.
"There weren't horrible things said about religions. So I have asked everybody to be a bit careful with these statements."
One opposition negotiator who had initially felt Brahimi's background as a foreign minister for a military-led government in Algeria might prejudice him against the rebels said he could not fault him for any bias during the talks.
"We would have rather preferred if we had a mediator without ties to an autocratic regime, who came from a neutral country with respect for human rights. But he has shown impeccable neutrality," the opposition negotiator said.
"He wants a deal."