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The moment Nigeria's Islamists graduated from local to international threat can be dated almost precisely, to just before 11 a.m. on Aug. 26. Mohammed Abul Barra, 27, a car mechanic and father of one from Maiduguri in Nigeria's northeast, had just turned into the diplomatic enclave in Nigeria's hot, dusty capital, Abuja. As he passed by embassies and empty lots, Barra presented an unremarkable sight: his car was a Honda Accord sedan, and Barra dressed and drove conventionally. The first indication of anything unusual was when he swerved into the exit lane of a 100-m driveway leading to U.N. House, the international organization's four-story headquarters. He bounced over one speed bump, then another. Then he drove straight at a 3-m sliding steel security gate, hitting its right edge so that it popped off its rail and fell harmlessly to one side. Barra repeated the maneuver with a second gate a few meters on and, the way now clear, drove on at U.N. House with the same deliberate, unhurried speed. He crashed into the lobby. The car, finally halted by a wall, bounced back. Barra did not try to get out. To one side, a security guard stood frozen. Others — U.N. staff, security personnel — ran away, then turned back. Barra stayed at the wheel. "Was he having second thoughts? Was he praying?" asks U.S. Ambassador Terence McCulley in Abuja, reconstructing the scene based on surveillance-camera footage he has viewed. "Was he searching for the detonator?" After a full 16 seconds, the car exploded.

Debris killed perhaps a dozen people. Most of the other 24 dead and 115 wounded, nearly all Nigerian, suffered massive internal injuries as a blast wave big enough to flatten a water tower 100 m away crushed their insides. An FBI forensic team later determined the bomb was colossal, and clever. Around 150 kg of plastic explosives had been placed inside a metal cone — a shaped charge — to focus its force. "This was very, very carefully planned," says Nigeria's national-security adviser, General Andrew Owoeye Azazi. "This was not just a local guy from Maiduguri."

The attack's ingenuity led many to conclude that Africa's nascent Islamic terrorism threat is metastasizing. The continent is home to three main Muslim militant movements. All are al-Qaeda "franchises," groups inspired by Osama bin Laden, even after his death, and his organization, even if they have no direct contact with it. All are also based in the Sahara or the Sahel, the semidesert that runs beneath it. In the scrub of northern Nigeria, a series of groups known collectively as Boko Haram have killed thousands — soldiers, police, civilians — in the past half-decade, and up to 600 this year. To their north, deep in the Sahara, al-Qaeda in the Islamic Maghreb (AQIM) is led by Algerian Islamists who kidnap and sometimes kill Westerners in Algeria, Mali, Niger and Mauritania. In the latest such attack, on Nov. 25, suspected AQIM militants kidnapped a Swede, a Dutchman and a South African from a restaurant in Timbuktu, Mali — and killed a German who refused to go along — a day after another group abducted two French geologists in the east of the country. In Africa's eastern deserts in Somalia, al-Shabab fights the official government and its protectors: African Union soldiers from Uganda and Burundi and, since October, an invading Kenyan force, plus, since November, an invading Ethiopian one. Like AQIM, al-Shabab has an international reach. Kenya blames it for several grenade attacks inside its borders. In July 2010, al-Shabab suicide bombers killed 76 people in the Ugandan capital, Kampala.

Terror on the Go
The Abuja attack suggests Boko Haram is linking to, and learning from, the two other groups. Nigeria's Azazi says before the attack he had intelligence of Boko Haram fighters traveling to al-Shabab strongholds in Somalia. A man who identifies himself as Boko Haram spokesman Abu Qaqa has also boasted to journalists of sending hundreds of fighters to train there. Boko Haram's links to AQIM are already well established. McCulley says the U.S. has seen reports of Nigerian militants traveling to northern Mali for training with AQIM since 2005. Certainly, the May kidnapping of a Briton and an Italian working for a construction company in northwestern Nigeria suggests AQIM's methods are spreading. In August, the pair appeared in a videotape sent to a news agency in which they identified their abductors as al-Qaeda.

Will Islamist insurgencies in Nigeria and Kenya — the economic powerhouses of West and East Africa — wreck Africa's nascent economic growth, just as the continent struggles to emerge from poverty and conflict? The Arab Spring seems to make al-Qaeda far less relevant, but does this coalescing threat make Africa a new battlefield in the fight against terrorism? The officer who heads Washington's Africa Command (Africom) thinks so. On Sept. 14, General Carter Ham told reporters in Washington: "If left unaddressed, you could have a network that ranges from East Africa through the center. Those three organizations have very explicitly and publicly voiced intent to target Westerners and the U.S. specifically. To me, that is very, very worrying."

Maiduguri, Barra's hometown, is on the southern edge of the Sahara in Nigeria's northeast. Hot, poor, and with some of the world's worst levels of education and health, Maiduguri has been a fount of Islamic revolution since the early 19th century, when Muslim rebels overthrew the ruling Hausa dynasties, accusing them of un-Islamic corruption. That dynamic — antiauthoritarian, revivalist Islamic movements challenging an avaricious, secular elite — endures. Its latest manifestation is Jama'atu Ahlis Sunna Lidda'awati wal-Jihad, Arabic for People Committed to the Propagation of the Prophet's Teachings and Jihad, better known as Boko Haram, meaning Western Education Is Sacrilege.

The movement has its religious foundation in the Izala sect, a group of Islamic preachers founded in the 1970s and led, by 2005, by a man called Mohammed Yusuf, who had studied in Saudi Arabia. Why bother with Western education, Yusuf would ask in sermons, when there were no jobs even for graduates? Hadn't Western influence given them Ali Modu Sheriff, a state governor who spent little on his people but built himself a palace of marble pillars and golden gates in Maiduguri? Yusuf set up a camp called Afghanistan to train volunteers for his revolution.

The spark for a full-fledged insurgency came in late July 2009. After a clash between police and Boko Haram members resulted in three deaths, riots erupted across northeast Nigeria. On July 28, the army surrounded Yusuf's compound in Maiduguri, arrested him, then executed him. By July 29, 700 people were dead, including enough militants to stall Boko Haram's insurgency. But by 2010, Boko Haram was back. This Nov. 5, at least 67 people died in a Boko Haram attack on the city of Damaturu.

One mistake made by both sides in the wars that followed 9/11 was how they often overlooked the detail and peculiar dynamics of the places in which they fought. In Afghanistan, the U.S. initially all but equated al-Qaeda and the Taliban, and in Iraq many Americans saw little difference between Osama bin Laden and Saddam Hussein. For their part, many Muslims still regard 9/11 and the 1997 death of Diana, Princess of Wales, as evidence of a global anti-Islamic conspiracy.

Will Africa make the same mistakes? Nigeria's President Goodluck Jonathan certainly seems susceptible. Rather than focusing on addressing Boko Haram's grievances regarding underdevelopment and corruption, Jonathan — a Christian from southern Nigeria — describes his country as an unfortunate bystander caught in the cross fire of an international war. Boko Haram are "just like other terrorist attacks in the world," he said on Nov. 10.

If you misread a problem, you can't fix it. If you mischaracterize a local Islamist rebellion as global terrorism, that's eventually what you'll face. "Left to stew, this trend of internationalization is inevitable," says a Western diplomat in Abuja. The Abuja bomb is proof that the causes of Nigeria's militancy have been left unaddressed for long enough that some fighters are now thinking bigger, and Jonathan's misperception is becoming a self-fulfilling prophecy. National-security adviser Azazi says the attack was most likely carried out by a Boko Haram faction led by a man called Mamman Nur, whom he describes as having sophisticated bombmaking skills and links to Islamists in Mali, Algeria, Somalia and Yemen. "Look at what happened between the crackdown in 2009 and their return in 2010," says Azazi. "Suddenly they can do IEDs [improvised explosive devices] and wire cars. This is something that's been festering — and is suddenly exploding."

The Somalian Connection
If Nigeria's Islamist militants are in transition to becoming an international threat, Somalia's made the leap long ago. The 1998 bombings of U.S. embassies in Nairobi and Dar es Salaam, Tanzania, which killed 230 people, were carried out by an al-Qaeda franchise based in Somalia. In 2006-08, the U.S. says, dozens of American, British, Scandinavian and Australian ethnic Somalis arrived in Somalia and joined the country's latest iteration of Islamist militancy, al-Shabab. That group, and a network of Ugandan and Kenyan jihadists they built, according to both the U.S. and a report by a panel of U.N. Somalia experts, was behind the 2010 Kampala bombings.

All that experience of extremism hasn't always made those fighting it any wiser. Proof of that lies behind a cage door at the back of the pink offices of the National Somali Security Intelligence, next to the presidential palace in Mogadishu. The door opens into a staircase leading down to a basement. At the bottom, according to one source, is another metal door that opens into a central corridor, flanked by 14 jail cells. There is no light, no windows, and the floors and walls are filthy. The place stinks.

The 50 men held there are all terrorism suspects abducted from across East Africa by security services working with the U.S. Ahmed Abdullahi is an ethnic Somali with one leg who was snatched from Nairobi by Kenya's security services in September 2009. "They came to my place in Nairobi, kicked my door down, blindfolded me and took me to the airport and on to Mogadishu," he says. On arrival, he says, he was interrogated by Somalis and unidentified Western personnel for a few weeks. They then lost interest. Abdullahi's been held ever since. "No one gets out of here," says the 26-year-old. "They don't know what to do with me. They can't let me out and risk me talking about this place."

TIME learned of this secret underground prison in Mogadishu, and Abdullahi's account of East African rendition, through a freelance photographer from Mogadishu, Mohamed Dahir, who has been briefly jailed there, twice. The second time, this March, Dahir was accused of belonging to al-Shabab. In the underground jail, he met Abdullahi, whom he recognized from Nairobi. Dahir also saw five white men — dressed in combat gear and carrying weapons — at the compound. That night, Dahir persuaded a guard to call his clan elders. They vouched for him, and he was released the next day. His captors apologized but warned: "Don't tell anyone what you saw here. We can get to you wherever you are." Dahir's account conforms to a pattern, documented in previous TIME reports and by human-rights groups, of forced rendition of hundreds of terrorism suspects from Kenya and Somalia to jails in Kampala and Addis Ababa.

Kenya is making other mistakes too in its own war on terrorism. On Oct. 16 it sent around 2,000 soldiers into Somalia in pursuit of al-Shabab. Kenya's attack was ostensibly in retaliation for the killing of a British tourist, the kidnapping of two more — a Briton and a French woman, who later died — and the abduction of two Spanish aid workers, all of which Kenya blamed on al-Shabab. U.S. diplomatic cables revealed by WikiLeaks show that Kenya has, in fact, been planning such an incursion for years. Its long-term Somali strategy — using southern Somalia's clans, the country's last real authority — to create an autonomous buffer state in the south has some merit, but al-Shabab has melted away and the advance has been slow. Kenya is also ignoring well-founded suspicions that the foreigners were snatched by professional kidnappers, and dismisses doubts over its military strategy, such as the wisdom of attacking al-Shabab's 2,500 fighters — fighters who saw off a much larger Ethiopian force in 2009 — with fewer than 2,000 men, or doing so in the rainy season, or during a famine, which war can only exacerbate. E.J. Hogendoorn, Horn of Africa specialist for the International Crisis Group, says: "A lot of analysts, myself included, fear Kenya is going to get bogged down in a much more prolonged occupation — and that's going to cost them a lot in blood and treasure, and, of course, has the potential to create a backlash from Somalis."

An Elusive Target
There remains hope that Africa can fare better in its fight against terrorism. By joining the dots across Africa, U.S. General Ham may be speculating about the future, rather than describing present reality. "Ham overstated," says a Western diplomat in Abuja. "He's extrapolating. We see training. We do not see operational links."

The threat from AQIM is also not straight terrorism. The group has, it is true, been bolstered by an influx of hundreds of pro-Gaddafi Nigerian and Chadian fighters from Libya, carrying weapons and cash. But Gaddafi opposed Islamic fundamentalism. AQIM's declared focus on religion may be a veneer for its real mission: crime. Since it was founded in 2003, the group has earned tens of millions of dollars in ransom, but politically it remains focused on Algeria rather than the global jihad. Jean-Pierre Filiu, a French al-Qaeda scholar, asks: "How much you do business to finance jihad, and how much you do jihad to justify your business?" For policemen, crime is a problem. For terrorist hunters, it's reassuring. It's hard to talk down a suicidal jihadist, but a businessman, of any sort, lives by his deals — of the kind, for instance, that persuaded southern Somali warlord Sheik Ahmed Mohammed Islam ("Madobe") to defect from al-Shabab earlier this year.

Crucially, some terrorist hunters have learned lessons from the decade that followed 9/11. The structure of Ham's command, Africom, shows insight. Africom employs aid specialists alongside soldiers, and stresses intelligence sharing, advisers and training over armed confrontation. Those are so far limited to one theatre — Somalia — and one type of strike: assassination, by drones, missiles or attack helicopters. Kenya's military spokesman Major Emmanuel Chirchir agrees with the need to "think bigger" in the fight against al-Shabab. Nigeria's Azazi even accords the enemy some respect. "I have had communication with a few of them," he says. "If we can't offer them jobs and good leadership, we cannot solve this problem."
— with reporting by Alan Boswell / Nairobi and Miamey, Mohamed Dahir / Mogadishu and Karen Leigh / Ouagadougou

• Alex Perry / Maiduguri
• Boko Haram and other African terrorist groups inspired by al-Qaeda are gaining strength, sophistication and global ambitions