Triumphant rebels seized Muammar Gaddafi's compound in Tripoli on Tuesday after a fierce battle with a loyalist rearguard but there was no word on the fate of the Libyan leader who vowed again to fight to the end.

Reuters journalists watched rebel fighters stream through the sprawling Bab al-Aziziya headquarters compound, firing in the air in celebration after hours of heavy clashes. But it was unclear whether the Brother Leader or his sons were still somewhere in the complex's maze of buildings and bunkers.

Defensive fire died away and hundreds of jubilant rebels poured in. Some smashed a statue of Gaddafi. Others hunted through dozens of buildings, unchallenged, seizing weaponry and vehicles. The rebels' envoy to the United Nations said the area was totally in the hands of the revolutionaries.

One man shouted: It's over. Gaddafi is finished.

The Russian head of the World Chess Federation, who visited Gaddafi in Tripoli in June, said he had received a call from him on Tuesday afternoon in which Gaddafi said he was still in the capital. He is in Tripoli, he is alive and healthy and is prepared to fight to the end, Kirsan Ilyumzhinov told Reuters.

The rebels' envoy in Rome, Hafed Gaddur, said: It seems clear that he is confined to his bunker complex.

We thought Tripoli would be liberated in one month or perhaps even two months, instead that happened in just a few hours, a day, so we've made great progress, he told Reuters.

Western governments, which have backed disparate opposition groups, said they could not be sure where the 69-year-old leader was but urged him to surrender after six months of civil war which have put an end to his four decades of absolute power.

French President Nicolas Sarkozy said after speaking to U.S. President Barack Obama that the end of Gaddafi's rule was inevitable and near.

NATO, which declined to confirm reports that its air forces bombed Gaddafi's compound to aid the rebels, said Gaddafi's whereabouts were unclear but no longer a major concern.

In Washington, a Pentagon spokesman said he believed Gaddafi was still in Libya and that his forces remained a threat. He also said the United States was monitoring chemical weapons sites in Libya, amid worries that groups hostile to Western interests could try to seize stocks once built up by Gaddafi.

SWIFT END SOUGHT

Western leaders are anxious for a rapid end to fighting -- tensions among rebels are a concern for those hoping for a swift return of order and a reopening of Libyan oil exports.

We hope this is over soon, said an unemployed engineer watching events near Gaddafi's compound. I fear that the violence will continue until Gaddafi and his family have left the country, he added, giving his name only as Omar.

Another bystander said: Gaddafi is finished, even if some snipers and mercenaries are still resisting. But there is no doubt that we are free and Gaddafi is finished.

There are growing concerns for civilians in the city, after days of siege and fighting in which officials have suggested hundreds of combatants may have been killed or wounded.

At a private house several miles from the center, wounded from the fighting were being treated, to the sound of gunfire.

We need medication and stretchers, this situation is a disaster, medical student Shuaib Rais told Reuters.

CREDIBILITY

Speaking after Gaddafi's son and long-time heir-apparent Saif al-Islam confounded rebel claims of his capture by appearing to journalists at the Bab al-Aziziya compound early on Tuesday, several analysts said the credibility of the disparate opposition movement had suffered a serious setback.

Though the credibility of Saif al-Islam's claims that his father's supporters were winning the war was also threadbare, confusion among the rebels, who seemed to have allowed two of Gaddafi's sons to escape on Monday, embarrassed their backers.

Noman Benotman, senior analyst at Britain's Quilliam think tank and an associate of Gaddafi's former spy chief, said: Gaddafi is banking on the rebels making a mess of Tripoli and causing chaos. He is relying on them to behave badly.

They want rival militia zones to start springing up ... That's why it's critical for the rebels to get their act together.

Residents, many of whom had taken to the streets on Sunday to celebrate the end of Gaddafi's 42-year rule, stayed indoors as the irregular rebel armies that swept the capital ran into resistance from sharpshooters, tanks and other heavy weaponry.

DIVISIONS

The lack of clear control, however, has revived concerns the sprawling, thinly populated desert state could fall into the kind of instability that has beset Iraq since Saddam Hussein's overthrow. Gaddafi loyalists and anti-Western Islamists could exploit Libya's ethnic, tribal and political divisions.

Rebel officials say they have a force ready to impose order in the capital, as they have generally done in parts of the country they have taken since February. But it is not yet clear how they will handle traditional east-west divisions if they consolidate their grip on the country.

The uncharacteristically efficient rebel advance into the capital, coordinated with an uprising inside the city, seemed evidence to some analysts of the military advice and training Western and some Arab powers, including Qatar, have provided.

Many assume special forces are also active on the ground.

Outside powers, including U.S. President Obama, have been at pains to characterize the revolt against Gaddafi as quite different from the Western assault on Saddam, saying it is a home-grown uprising inspired by other Arab protest movements that overthrew Western-backed autocrats in Tunisia and Egypt.

Aid, some of it in the form of Libyan state funds seized from accounts controlled by Gaddafi, and advice will be plentiful, foreign governments assured the rebel leadership in Benghazi as it contemplates moving to Tripoli.

But all have ruled out sending in ground troops to bolster a new government which faces considerable difficulties in setting up a new administration given Gaddafi's four-decade reliance on informal governance and a personality cult.

We've sought to learn the lessons of the failures of Iraq, which have very much influenced our thinking -- trying to make sure we don't make the same mistakes again, said British International Development Secretary Andrew Mitchell.