With forces loyal to Muammar Gaddafi given until Saturday to surrender by Libya's rebel council, an expert tells Channel 4 News Gaddafi must now realise that the conflict is over.
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Mustafa Abdel Jalil's ultimatum comes after rebel forces stormed Tripoli last week, breaking into Colonel Gaddafi's compound and bringing to a climax a six-month uprising against his 42-year rule, backed by a Nato mission to protect civilians.
The whereabouts of the colonel himself remain unknown, although some members of his family have fled to Algeria. His wife and three of his children entered the country on Monday, the Algerian foreign ministry confirmed.
Mr Abdel Jalil told a press conference that the rebels wished to bring an end to the uncertainty in Libya.
Read more: Where are the Gaddafis?
"By Saturday, if there are no peaceful indications for implementing this, we will decide this matter militarily. We do not wish to do so but we cannot wait longer," he said.
Rebels are currently advancing on Sirte, Gaddafi's birthplace, one of a handful of towns which remain loyal to the Libyan leader. Fighters have stopped short of an all-out assault in the hope that a surrender can be negotiated.
The surrender deadline is part of wider attempts by the National Transitional Council (NTC) to establish order in Libya after last week's frenzied fighting in Tripoli.
They plan to move their headquarters to the capital from Benghazi later this week to get the country back on its feet after months of violence.
The capital itself - housing two million people - remains without running water or electricity, and many shops, banks and pharmacies are still closed.
Read more from Alex Thomson on Tripoli's Gangsta's Paradise
Where is Gaddafi?
While the NTC tries to establish order in Libya, the country's former leader appears to have completely disappeared.
Libya expert Dr Imad El-Anis, of Nottingham Trent University, told Channel 4 News that whether or not Gaddafi is ever apprehended depends on whether he can bring himself to run away.
"He probably still has some finances and some friends, both in Libya and further afield," said Dr El-Anis.
"It's more a case of whether he wants to go or not - and if he goes somewhere, he will be running away. He must realise that he has no hope any more, that this conflict is over. It's lost to him.
"He's always said he will be a martyr, and stay and die in Libya - dictators tend to talk about that a lot, then they end up being as cowardly as anyone else."
But he said predicting where Gaddafi was would be a thankless task, particularly in a conflict which has been as unpredictable as this one. He said the former leader could have left the country weeks ago - or still be hiding in Libya.
"I could see him being apprehended in Libya, dying in Libya. But at the same time there have been so many surprises in the last six months, he could turn up in Angola, Venezuela, Zimbabwe, and it wouldn't be that much of a surprise."
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