The French or African troops who hunt down the militants holed up in the mountains and deserts of northeast Mali may find a resilient enemy capable of fighting back with a concealed arsenal of surprising firepower.

France’s initial success in its three-week old intervention in its former colony has gained Paris plaudits at home and abroad as a welcome blow struck against militants threatening Africa and the West.

Timbuktu and Gao, the main Malian towns held by insurgents since last year, fell to the French at the weekend, and French troops also seized the airport at Kidal, the last urban bastion abandoned by the rebels.

But the next step in stabilizing Mali and pursuing the Al-Qaeda-allied fighters in their remote desert and mountain bolt holes near Algeria’s border looks like a much tougher task.

It will take longer than a few weeks and likely require a bigger and more international effort than the limited offensive that has so far involved 3,500 French soldiers on the ground, backed by warplanes, helicopters and armored vehicles. “Both politically and militarily, now is going to be the hard bit,” Gregory Mann, a Mali expert who is associate professor of history at Columbia University, told Reuters.

The rebel forces are thought to be sheltering north of Kidal in the Adrar des Ifoghas, a vast, rugged mountain buttress that has given sanctuary before to Al-Qaeda hostage-takers and Saharan traffickers of drugs, people and cigarettes. They are believed to have weapons, fuel and supplies hidden in caves, tunnels and rock strongholds. These were stashed away before their pell-mell retreat from relentless French airstrikes that left a trail of rebel charred vehicles and abandoned arms caches in dusty Niger River and Saharan towns. “This is where they have the bulk of the stuff hidden,” said Rudy Atallah, a former counterterrorism director for Africa at the US Department for Defense. “They have barrels of fuel and weapons. They have been preparing for a long time.”

Their preserved arsenal could include heavy machineguns, hand-held rocket launchers and also possibly one or more Grad multiple rocket launchers mounted on vehicles, according to arms experts who have viewed photos and footage of munitions caches abandoned by the rebels in their hasty withdrawal.

“This is pretty heavy ordnance, a level that would achieve parity with or even out gun most West African militaries,” James Bevan, head of Conflict Armament Research, said after viewing photos of a cache found at Diabaly in central Mali.

A Western security source, who asked not to be named, said air power would help in the next phase — but only so much. “Ground troops will have to go into the mountains and that will lead to casualties,” he said.

Guinea’s President Alpha Conde, whose West African country is offering troops to a UN-backed African intervention force being deployed in Mali, predicted a “battle in the Sahara” against what he called “narco-traffickers” and “terrorists.” “The rebels will not disappear into the sky,” he said last week in Davos, Switzerland.

“If we don’t want the Sahara to become Afghanistan, then we need the world to get involved, not just France and Africa but also the United States and the European Union,” he added. But the United States and Europe, where a recession-hit public has little appetite for overseas wars after Iraq and Afghanistan, have ruled out sending combat troops and offer instead training as well as logistical and intelligence support.

French President Francois Hollande, anxious to reassure his people France will not get bogged down in a messy war in a faraway former colony, has said he expects African forces to take over the job of hunting down the rebels in the north. It is hard to know exactly what materiel and manpower the rebels have lost in hundreds of French airstrikes that are now homing in on rebel positions north of Kidal.

A French military video showed a rebel Grad multiple rocket launcher destroyed near Gao. French estimates speak of several dozen rebels killed in the limited direct clashes so far. The real figure could be higher given the intensity of the airstrikes.

Estimates by some security experts had put the combined original strength of the rebel alliance in northern Mali, which groups Al-Qaeda’s North African wing AQIM, Malian group Ansar Dine and AQIM splinter MUJWA, at around 3,000 fighters.

Mark Schroeder, director of Sub-Saharan Africa analysis at Stratfor consultancy, believes France and its allies will try to prevent rebels from fleeing over Mali’s porous Saharan borders into neighboring states such as Algeria, Niger and Libya.

“If AQIM can be degraded ... forced into a space from where they can offer no threat, that can be a success,” he added.

Nearly 2,000 troops from Chad and Niger, with experience of fighting in the Sahara, are backing up the French and Malians as they consolidate their gains in Gao and Timbuktu and also push reinforcements up toward Kidal in the wild northeast.

“The military cycle is far ahead of the political cycle ... They are liberating more than they can occupy,” Mann said.

He added Malian authorities also needed to be pragmatic in handling fickle pro-autonomy northern Tuareg rebels, many of them experienced desert fighters, who have offered to help the French-led offensive against Al-Qaeda and its allies.