Those now in power led the rebel army that drove out the Hutu killers in 1994.
In Rwanda in 1994, the world watched while the Hutu majority slaughtered some 700, 000 Tutsis.
Under threat from Hutu extremists, they believe they must have military control to survive.
Nkunda says his forces are fighting to defend Congolese Tutsis from Hutu militants who escaped to Congo.
He said the rebel Hutu groups so far excluded from earlier talks would no longer be "ignored".
The strongest support for Mr Mandela's peace plan comes from the predominantly Hutu Burundian Democratic Front (Frodebu).
Burundian officials say that Rwanda's Hutu militiamen, the interahamwe, were responsible for much of the recent killing around Bujumbura.
He joined the Hutu rebellion in 1995 and rose through the ranks to become head of the FDD in 2001.
Rwandan Hutus remained in the jungles of eastern Congo, where they preyed on local residents and participated in Hutu militias.
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At the time, Nkunda said his forces were fighting to defend Congolese Tutsis from Hutu militants who escaped to Congo.
The Rwandans are the soldiers of the former Hutu government who fled to Zaire, together with genuine refugees, in 1994.
Despite its past as a Hutu rebel group, the movement claims to have rapidly recruited Tutsis since becoming a political party.
Although he signed the deal, Gen Nkunda has always refused to disarm while Rwandan Hutu rebels still operate in the area.
Four Hutu deputies have already been thrown out of both their party and the assembly, accused of identifying with old-style extremism.
She is also accused of transferring money to the mainly ethnic Hutu FDLR rebels, based in neighbouring Democratic Republic of Congo.
The two Hutu rebel groups, who remain outside the peace process, have been fighting against the minority Tutsi dominated army since 1993.
Some moderates from the Hutu majority who supported Tutsis were also killed.
If Mr Buyoya stayed on, it would stir many Hutus to shift their support from peaceful Hutu parties to violent rebel groups.
Under the power-sharing deal, Tutsi President Pierre Buyoya is due to swap places with his Hutu Vice-President Domitien Ndayizeye on 1 May 2003.
He was defence minister from 2000 until November last year, when Rwandan spokesman Joseph Bideri said he was sacked for his "extreme pro-Hutu" views.
Under the power-sharing agreement, President Pierre Buyoya is due to step down and be replaced by Hutu Vice-President Domicien Ndayizeye in April next year.
In the early 1990s ethnic Tutsi rebels from both sides of the border had fought the Hutu-led Rwandan government, which was supported by Mobutu.
This could bring them into the Hutu-Tutsi wars, on different sides.
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In the late 1950s and early '60s, Kagame's family and other Tutsis were under siege as Hutu gangs went from village to village, pillaging and killing.
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The 2005 vote was one of the final steps in a peace process intended to end years of fighting between Hutu rebels and the Tutsi-controlled army.
Mr Annan warned the Security Council that Burundi's Tutsi elite and the Hutu majority were "locked in implacable hostility to one another" with steadily rising violence.
What, meanwhile, has happened to the Hutu militiamen whose presence in eastern Congo was the reason Rwanda and Uganda gave for intervening in the first place?
The National Alliance for Change brings together the two former presidents Mr Buyoya deposed, Jean-Baptiste Bagaza and Sylvestre Ntibantunganya, one a Tutsi and one a Hutu.
The Belgians then switched their alliance to the new Hutu regime, and by the time they left in 1962, Rwandan society was severed by ethnic conflict.
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Almost everyone agrees that reining in the various Hutu militias, especially the FDLR, is a necessary step if relations between Kigali and Kinshasa are to be improved.
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