Even for the likes of al-Qaeda, an organization not known for its warm and fuzzy side, al-Zawahiri has a reputation for obnoxiousness. One ex-militant describes al-Zawahiri, 60, as "sharp-tongued" and "arrogant." His scraggly beard, prayer callous on his forehead and thick glasses make him look more like an unpleasant and pious schoolmaster than a terrorist mastermind. Nevertheless, al-Zawahiri remains a force to be reckoned with. The Egyptian fully intends to continue waging bin Laden's war against the U.S. and its allies, his hatred sharpened by the fact that his wife and two children were killed by a U.S. air strike in October 2001 while fleeing across Afghanistan.

Despite the Egyptian's fulsome eulogy for his boss earlier this month, the take-charge deputy was often at odds with bin Laden. Hothaifa Abdullah Azzam, a Jordanian cleric who spent time in Peshawar, Pakistan, and who maintains communication with some fighters of al-Qaeda told TIME in Amman that by 2006, al-Zawahiri and his comrades were "isolating bin Laden with the excuse of protecting him." He adds, "Nobody I met liked al-Zawahiri, but he is the guy moving things." Azzam also says that bin Laden and al-Zawahiri quarreled in 2007 over the choice of a new military commander after the previous one was killed. "Al-Zawahiri got his way and bin Laden was not happy." The new commander is thought to be either Saif al-Adel, a former Egyptian commando, or a Libyan, Abu Yahya al-Libi.

Al-Zawahiri's abrasiveness is one factor to explain why he was not automatically picked to replace bin Laden by al-Qaeda's ruling council, the so-called General Command. Another is his lack of combat experience. A former surgeon and ideologue, al-Zawahiri has a reputation for leading from the rear. "He's called the 'Shadow Leader,'" says Azzam. Furthermore, a new, younger generation of combat-hardened jihadi leaders from Libya and Yemen are rising through the ranks, and their utterances on the Internet seem to have far greater impact than al-Zawahiri's oft-repeated rants against the Americans and the Jews.

Several weeks back, a few jihadi-militant websites claimed that the Egyptian al-Adel had been chosen as a "caretaker" chief, and it seemed that al-Zawahiri had been shoved aside. One Washington official who tracks al-Qaeda offered two scenarios to explain the need for a caretaker: either a succession battle was raging inside the terrorist group, or its commanders were too scattered after bin Laden's death to gather for a vote. Either way, says the official, "It underscores the fact that al-Zawahiri isn't well liked by the senior leaders or the foot soldiers."

Unlike bin Laden, who spent the past six years holed up behind the penitentiary-like walls of his Pakistan safe house, al-Zawahiri is a moving target. "His business cards are left all over the place," says South Asia expert Michael Semple, a fellow at Harvard's Kennedy School. By all accounts, the Egyptian has been moving around Pakistan's tribal borderlands and fleeing the predatory missiles of the drones.

Yet, even on the run, al-Zawahiri can't keep quiet. Since 2006, he has broadcast 22 anti-Western video sermons on the Internet, compared with a single appearance by his late boss. Earlier this month, in his first public response to bin Laden's death, al-Zawahiri proclaimed, "Today, and thanks be to God, America is not facing an individual or a group ... but a rebelling nation [a reference to the Muslim community] which has awoken from its sleep in a jihadist renaissance, challenging it wherever it is."

Al-Zawahiri is as deadly as he is elusive. Counterterrorism experts say that when bin Laden slipped into his Abbottabad villa, al-Zawahiri handled day-to-day operations for al-Qaeda and coordinated murderous attacks with the organization's Taliban allies. He roams inside a wide swath of Pakistan's mountainous border with Afghanistan, extending from Bajaur (where the widower may have married the daughter of a Pashtun chieftain) down to South Waziristan. This lawless region, says Semple, is "the world's greatest jihadi industrial park," from where al-Qaeda supplies "specialist services" to the various Pakistani and Afghan Taliban factions bent on committing spectacular suicide bombings and assassinations.

Al-Zawahiri was also involved in a trap against the CIA. A Jordanian "mole" planted by the CIA inside al-Qaeda promised to reveal al-Zawahiri's whereabouts in December 2009. Instead, the Jordanian turned out to be a triple agent, an unrepentant jihadi and suicide bomber, who blew up a high-level CIA team at a secret base near Khost, in eastern Afghanistan. Five CIA officers and two security men were killed and a dozen others were wounded in the bombing, the worst disaster to befall the agency in over 30 years. A U.S. official told TIME that al-Qaeda leaders had "knowledge of the operation and encouraged it." And the bait had been al-Zawahiri.

Questions have arisen over whether Pakistan's all-powerful military knew where bin Laden was holed up. But there's little doubt that, had the Pakistanis known where al-Zawahiri was hiding, they would have gladly hunted him down. Bin Laden, according to his biographer Michael Scheuer, an ex-CIA officer, had "close ties with ISI [Pakistani intelligence] up to and including generals" before 9/11. But al-Zawahiri had a phobia of military men, acquired during his years inside the prisons of the Egyptian regime.

Soon enough, al-Zawahiri's suspicion of the Pakistani army turned to hostility. In a September 2003 video harangue, the Egyptian terrorist urged Pakistanis to rise against the generals. Three months later, President Pervez Musharraf narrowly escaped two attempts on his life. Counterterrorism experts in Islamabad also claim al-Zawahiri was involved in the December 2007 assassination of ex-Prime Minister Benazir Bhutto. And U.S. officials say the Egyptian maintains close ties with Hakimullah Mehsud, leader of the Pakistani Taliban, which has launched a suicide-bombing campaign against Pakistani troops in the tribal territory bordering Afghanistan.

The CIA and the Pakistanis had plenty of near misses with al-Zawahiri. He was sighted in February 2003 with Khalid Sheikh Mohammed, a day before the alleged mastermind of the 9/11 attacks was captured in Rawalpindi in a joint raid by Pakistani and American forces. A year later, al-Zawahiri supposedly escaped with minor injuries after the Pakistani air force, following a tip-off from an informant, bombed a farmhouse in South Waziristan. The trail went cold for two years, until American intelligence got wind of a dinner feast for al-Qaeda's leaders north of the Khyber Pass. Predator missiles struck the gathering, killing 18 people. Al-Zawahiri was supposed to be among them, but apparently bowed out at the last minute.

But al-Zawahiri's hunters may have again picked up the trail. Using intelligence gleaned from computer files seized in bin Laden's Abbottabad safe house, U.S. officials say they may be closer to finding al-Zawahiri and other surviving al-Qaeda leaders.

Meanwhile, the situation may get complicated in Afghanistan if the U.S. and Afghan President Hamid Karzai choose to broker cease-fire talks with the Taliban, al-Qaeda's longtime ally. Both the Taliban and al-Qaeda hate the U.S., but they have divergent goals. It's al-Qaeda's strategy to keep the U.S. tied down in Afghanistan, while the Taliban wants to drive out the "infidel" American and NATO troops. Afghanistan, says Semple, has "turned into a giant film studio for al-Qaeda propaganda." He adds, "They want to keep America embroiled in the conflict." And so, if Karzai wants to reach a settlement with the Taliban, expect al-Qaeda to come between their erstwhile ally and the Afghan government, especially now that al-Zawahiri is running the show. — With reporting by Ranya Kadri/Amman

McGirk, a former TIME bureau chief, is currently a fellow at University of California, Berkeley's Investigative Reporting Program.