As usual, a well-trained Western army has gone through a fierce-looking but virtually untrained force of African rebels like a hot knife through butter. Two weeks ago, the northern half of Mali was entirely under the control of Islamist militants, whose forces were starting to advance into southern Mali as well. So France decided on very short notice to send troops and combat aircraft to its former colony in West Africa.

Today, every town in the north of Mali is under French control, and the surviving rebels have fled into the desert. But most of them did survive: after losing a couple of major clashes in the first days of the French drive northwards, the Islamist forces simply abandoned Gao, Timbuktu and Kidal, the main towns of the north, as soon as the French forces came near. The easy part of the intervention is now over.

It’s not surprising that the French military intervention was an instant success. The Islamist rebels, like most African paramilitaries (and quite a few African armies, too), did not even know the basic combat drills that every infantryman in a Western army has practised until they are second nature. But now come three tasks that are considerably more difficult.

The first is to deploy an African Union-backed military force, made up of units from armies elsewhere in West Africa, to take over from the French. You can’t just hand the recaptured towns back to Mali’s own army, which is so incompetent and rotted by politics that it would promptly lose them back to the militants.

This force, dubbed the International Support Mission to Mali, has the unanimous blessing of the United Nations Security Council. International donors met in Ethiopia on Tuesday and pledged $455.53 million to pay for this force. Mali’s many neighbours—it has open desert borders with seven other West African countries—have already identified the units they are going to send.

But it’s going to be weeks or months before those African units actually arrive, because many of them aren’t very well trained either. (French and British troops are being sent to train some of them before they even set foot in Mali.) In the meantime, the north of Mali will really be entirely under French military rule.

This means that there will be none of the looting, rape and murder that tends to follow the Malian army’s arrival in town, but the French troops are very foreign indeed. They are not even Muslims, in a country that is nine-tenths Muslim. They were welcomed as liberators when they rolled into the northern towns in the last few days, but if they stay for too long they will become first unpopular, and then hated. That’s just the way things work.

Once African troops replace the French, the next task is to rebuild the democratic government of Mali, which was destroyed by a military coup last March. The interim president, Dioncounda Traore, says that he wants to hold elections next July, but behind the scenes the greedy young officers who made the coup still hold the real power. They will have to be sent back to their barracks before elections take place, and that will not be easy.

And the third task is to win the very different kind of war that starts in Mali now. Retaking occupied towns was easy. Now that the militants have scattered across the vast deserts of northern Mali, they will launch a different kind of war—a “war of the shadows”, conducted by raids, bomb attacks and assassinations.

Countries can survive for decades with that kind of low-intensity war going on in the background, but the only way to shrink it to a manageable level is to make a political deal. This is not impossible in Mali, because the Islamist fanatics actually hijacked the revolution from their former allies, the Tuareg separatists.

Most of the people in the north are Tuaregs, desert-dwelling people of Berber stock and nomadic heritage who are ethnically, culturally and linguistically distinct from the black African majority in southern Mali. Many of them support the separatist movement that wanted to create an independent Tuareg state in northern Mali, but few actually share the extreme religious views of the Islamist militants.

The two groups made an alliance to drive the Malian army out of the north, but the Islamists then turned on their allies and seized absolute power for themselves. Their harsh rule was resented by most people, however, and so it should be possible to isolate the Islamists if the Malian government is willing to make a deal that gets the Tuareg separatists on its side.

They won’t get independence, but they would probably settle for a large degree of autonomy for the north. It will be hard to get a new Malian government that is elected almost entirely by the votes of southerners (90 percent of the population lives in the south) to make that concession, but the alternative is a long, draining guerilla war in the north.

Was the French military intervention in Mali necessary? Yes, in the view of the United Nations, the African Union, and most Malians. Was it a success? That remains to be seen.