Three of Muammar Gaddafi's sons are in custody as rebels say they hold 95 per cent of Libya's capital. President Obama says it is clear that Gaddafi's rule is over, but the fight in Libya is not.

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After the dramatic events today, which saw rebel convoys roll into Libya's capital Tripoli, the city is still wracked with gunfire - though Channel 4 News' International Editor Lindsey Hilsum reports "happy shooting" is also taking place and women and children are cheering the rebels.

In the US, the White House has said there is no evidence that Gaddafi has left the country, and earlier the rebel council said they did not know the whereabouts of the embattled leader.

However, President Obama made a statement on Monday evening, saying it is clear that Gaddafi's rule is now over, although the fight in Libya is not.

Elsewhere, there have been reports that the Libyan Prime Minister Al Baghdadi Ali al-Mahmoudi and the head of the country's television union, Abdallah Mansour, are on the Tunisian island of Djerba where Gaddafi's wife Safia and daughter Aisha fled in May.

Celebrations in Tripoli (Reuters)

On Monday morning, rebels and civilians waving opposition flags and firing into the air drove into Green Square, which they renamed "Martyrs Square", the symbolic location the government had until recently used for mass demonstrations in support of Gaddafi.

'Gaddafi is finished'

According to reports, a column of hundreds of rebel fighters and pick-up trucks carrying rocket launchers moved through the Libyan capital towards the central Green Square.

The rebels in the column were shouting "Allahu Akbar!" or "God is greatest!" One of the fighters, Walid Ahmed, said he left Tripoli three months ago to join the rebellion in the Western Mountains to the south. "Now I am back and Gaddafi is finished," he said.

Get the latest in the Channel 4 News Libya live blog

The day started with news that two of Gaddafi's sons have been captured by the rebels.

Rebel National Transitional Council Coordinator Adel Dabbechi said that Gaddafi's younger son Saif Al-Islam had been captured.

The International Criminal Court in The Hague, which wants Saif along with his father on charges of crimes against humanity, confirmed he had been held and said he should be handed over for trial.

But a source close to the rebel National Transitional Council has told Channel 4 News that the fate of captured members of Gaddafi's family was still uncertain. But the source said that the rebels' reluctance to hand over the pair to the International Criminal Court does not mean their lives are in immediate danger: "There is such a force of appetite in the country to see the Gaddafis stand trial and anything that gets in the way of that would not be seen well by the Libyan people."

The source said the reason for the delay is that some people would like to see the Gaddafis face Libyan rather than international justice and for Libyans to be seen to be exerting control over their own country.

Channel 4 News' International Editor Lindsey Hilsum is in Tripoli. She writes:

From balconies and windows, women and children are waving and cheering the fighters. An old man over the side of the road watched the heavily armed convoy of rebels drive into town from the Nafusa mountains and said: "They are all my sons". I asked one man: "Where is Gaddafi?" He replied: "Gone with the wind."

Follow updates from Lindsey on Twitter: @lindseyhilsum

Chairman of the National Transitional Council Mustafa Adbel Jalil (Reuters)

World leaders' reactions

After a meeting of the UK's National Security Council on Libya, Prime Minister David Cameron urged Colonel Muammar Gaddafi to stop fighting as the Libyan dictator's regime was in "full retreat".

"His regime is falling apart and is in full retreat," Mr Cameron said. "Gaddafi must stop fighting, without conditions, and clearly show that he has given up any claim to control Libya."

He added that Gaddafi's future should be put in the hands of the new Libyan authorities. And US President Barack Obama said Gaddafi's rule was showing signs of collapse and called on him to quit now to avoid further bloodshed.

He said in a statement: "The surest way for the bloodshed to end is simple: Muammar Gaddafi and his regime need to recognise that their rule has come to an end.

"Gaddafi needs to acknowledge the reality that he no longer controls Libya. He needs to relinquish power once and for all."