BBC
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A National Transitional Council (NTC) official told the BBC the bodies were buried at dawn in an unknown location.
This follows days of apparent uncertainty among the new leadership about what to do with the bodies.
Gaddafi's family wanted them buried outside the former leader's hometown of Sirte.
NTC leaders had expressed a preference for a secret burial.
Late on Tuesday, Dubai-based TV channel al-A'an broadcast footage it said showed Gaddafi's funeral.
The footage, which was filmed at night, shows a group of men dressed in civilian clothes walking around three wooden coffins.
A man is seen tucking in the traditional white cloth used to wrap bodies according to Islamic burial custom.
The pictures have not been independently verified.
Bound by Fatwa
Officials have given few details of the ceremony.
They say it took place early on Tuesday. A few relatives and officials were in attendance and Islamic prayers were read.
"It says that his body should not be buried in Muslim cemeteries and should not be buried in a known place to avoid any sedition," Mr Shammam said.
An NTC official had earlier told Reuters news agency that Col Gaddafi would be buried in a "simple" ceremony with "sheikhs attending" on Tuesday.
"It will be an unknown location in the open desert," he said, adding that a burial was needed because decomposition of the body had reached the point where the "corpse cannot last any longer".
Gaddafi, Mutassim and former Defence Minister Abu Bakr Younis Jabr were killed on Thursday following the fall of Sirte, the last major pro-Gaddafi bastion.
Witnesses said the bodies had been removed late on Monday from the meat storage warehouse in Misrata where they had been on display.
The BBC was told prayers were said over the bodies before they were driven away.
"Our job is finished," a security guard at the warehouse, Salem al Mohandes, told the Arabic television station al-Jazeera. "[Gaddafi] was transferred and the military council of Misrata took him away to an unknown location."
Shrine fears
The BBC's Katya Adler in Tripoli says the question of how to dispose of Gaddafi's body has been a political minefield for the new Libyan leadership, and is the reason why it has taken four days for a decision to be taken.
Islamic tradition dictates a burial should happen within a day of the death.
But the NTC leadership was concerned that any public grave could become a shrine for Gaddafi loyalists or a target of hatred for those who opposed his regime, our correspondent says.
In the end, she adds, the decomposition of the body meant the NTC had to act.
Questions have been raised over the former leader's death after video footage showed him alive at the time of capture. Officials said he had been killed subsequently in a crossfire.
A post-mortem examination carried out on the 69-year-old's body on Sunday showed he had received a bullet wound to the head, medical sources said.
Acting Libyan leader Mustafa Abdul Jalil said the NTC had formed a committee to investigate the circumstances surrounding his death.
Meanwhile another of Gaddafi's sons, Saif al-Islam, remains at large. He is believed to have fled towards the desert border with Niger.
A Niger official said Saif al-Islam Gaddafi was travelling with ethnic Tuaregs - who were among Gaddafi's supporters.
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Footage apparently showing the Gaddafi bodies being prepared for burial has been released
The bodies of ex-Libyan leader Muammar Gaddafi, his son Mutassim and a top aide have been buried in secret in the desert, Libyan officials say.
This follows days of apparent uncertainty among the new leadership about what to do with the bodies.
Gaddafi's family wanted them buried outside the former leader's hometown of Sirte.
NTC leaders had expressed a preference for a secret burial.
Late on Tuesday, Dubai-based TV channel al-A'an broadcast footage it said showed Gaddafi's funeral.
The footage, which was filmed at night, shows a group of men dressed in civilian clothes walking around three wooden coffins.
A man is seen tucking in the traditional white cloth used to wrap bodies according to Islamic burial custom.
The pictures have not been independently verified.
Bound by Fatwa
Officials have given few details of the ceremony.
They say it took place early on Tuesday. A few relatives and officials were in attendance and Islamic prayers were read.
Continue reading the main story 
The tussle over the body was between the Misratan military brigades who captured and killed Col Gaddafi on Thursday and the politicians - the National Transitional Council - who are now trying to take charge of the whole of this country.
The body of Col Gaddafi was the number-one war trophy after eight months of civil war.
The tussle over it was all part of a behind-the-scenes positioning for power in the new Libya that we'll probably see the aftershocks of reverberating out in the weeks and months to come.
Analysis
The body of Col Gaddafi was the number-one war trophy after eight months of civil war.
The tussle over it was all part of a behind-the-scenes positioning for power in the new Libya that we'll probably see the aftershocks of reverberating out in the weeks and months to come.
Libya's Minister for Information Mahmoud Shammam said the NTC was following a fatwa, or religious ruling.
An NTC official had earlier told Reuters news agency that Col Gaddafi would be buried in a "simple" ceremony with "sheikhs attending" on Tuesday.
"It will be an unknown location in the open desert," he said, adding that a burial was needed because decomposition of the body had reached the point where the "corpse cannot last any longer".
Gaddafi, Mutassim and former Defence Minister Abu Bakr Younis Jabr were killed on Thursday following the fall of Sirte, the last major pro-Gaddafi bastion.
Witnesses said the bodies had been removed late on Monday from the meat storage warehouse in Misrata where they had been on display.
The BBC was told prayers were said over the bodies before they were driven away.
"Our job is finished," a security guard at the warehouse, Salem al Mohandes, told the Arabic television station al-Jazeera. "[Gaddafi] was transferred and the military council of Misrata took him away to an unknown location."
Shrine fears
The BBC's Katya Adler in Tripoli says the question of how to dispose of Gaddafi's body has been a political minefield for the new Libyan leadership, and is the reason why it has taken four days for a decision to be taken.
Islamic tradition dictates a burial should happen within a day of the death.
But the NTC leadership was concerned that any public grave could become a shrine for Gaddafi loyalists or a target of hatred for those who opposed his regime, our correspondent says.
In the end, she adds, the decomposition of the body meant the NTC had to act.
Questions have been raised over the former leader's death after video footage showed him alive at the time of capture. Officials said he had been killed subsequently in a crossfire.
A post-mortem examination carried out on the 69-year-old's body on Sunday showed he had received a bullet wound to the head, medical sources said.
Acting Libyan leader Mustafa Abdul Jalil said the NTC had formed a committee to investigate the circumstances surrounding his death.
Meanwhile another of Gaddafi's sons, Saif al-Islam, remains at large. He is believed to have fled towards the desert border with Niger.
A Niger official said Saif al-Islam Gaddafi was travelling with ethnic Tuaregs - who were among Gaddafi's supporters.
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