Having routed the Zairean army (FAZ) last month and established a swathe of liberated territory in the east, they intend to overthrow the Zairean President Mobutu Sese Seko, who remains in the south of France recovering from a cancer operation.
What might a couple of months ago have been dismissed as a localised self-defence campaign has grown into a movement with strong national aspirations. As evidence of their seriousness, the rebels have named the area under their control Democratic Congo. The Zaire river - which they have yet to reach - has reverted to its earlier name, Congo.
"The word Zaire means nothing in any of our languages," said a rebel spokesman. "This is the Congo,this nation should be the Democratic Congo. Soon we will liberate all of Zaire, and again we will be the Congo."
Zairean soldiers, unpaid for months and short of food, are retreating further into the interior. Missionaries leaving the region report widespread looting and raping by the demoralised FAZ.
According to the rebel military commander, Andre Ngundu Kissasse, who was speaking in the eastern border town of Goma at the weekend, more than 300 Zairean government troops have defected to the rebel side.
Though they speak a number of different languages, the rebels have proved a cohesive fighting force. From an initial core of ethnic Zairean Tutsis, called Banyamulenge, they have formed a broad-based movement comprising guerrilla groups with roots in post-independence nationalism, and disaffected tribes. Calling themselves the Congolese Liberation Army (CLA), they have at their head a former Marxist freedom-fighter, Laurent Kabila.
The Tutsi-controlled government of neighbouring Rwanda is widely believed to provide the insurgency's support and motivation. The most compelling circumstantial evidence lies in the significant number of English-speakers among the rebels; English is the lingua franca of the new order in Rwanda but not widely used in Francophone Zaire. Nevertheless, both the Rwandan government and the CLA continue to deny any links.
Also accused by Zaire of backing the rebels are the Tutsi-dominated regimes in Burundi and Uganda, whose army recently launched incursions into Zaire. The Zairean government charges Rwanda, Burundi and Uganda with attempting to establish a "Tutsi empire" in central Africa. Mr Kabila, however, insists his movement is independent of regional backing.
The rebels have captured large stocks of FAZ weapons to add to the arms they bought from unpaid Zairean troops before launching their insurgency in September.
The rebels have appointed civilians to administrative posts in parts of the territory they hold and in the main eastern towns of Goma, Uvira and Bukavu, life is returning to normal, with businesses and markets open.
Mr Kabila says he intends to form a new government but has ruled out talks with ailing President Mobutu whom he views as a crook and a tyrant. Mr Kabila, who favours a free-market economy, says he wants Zaire's vast mineral wealth to benefit the people who are among the poorest in the world.
The CLA claims to have already taken a number of mines, including the diamond mines around the town of Kindu and President Mobutu's personal gold mine near Bunia.
Whether the insurgents are strong enough to overcome the huge military and geographic obstacles before them remains to be seen. It is also unclear whether they can continue to count on popular support as they push further into Zaire's interior. The closer the rebels get to Kinshasa, the greater will be their need for assistance from other opposition groups within Zaire.