The announcement by Iraqi Prime Minister Nouri al Maliki that the two top leaders of al Qaeda in Iraq have been killed after a very long manhunt was greeted by many al Qaeda watchers with skepticism. The Iraqi government and the American military have claimed to have killed Abu Ayub al Masri, the Egyptian leader of al Qaeda in Iraq, more than once in the past. Abu Omar al Qureshyi al Baghdadi, the leader of al Qaeda’s self proclaimed Islamic State in Iraq has also been reported dead or captured several times in the last few years. At other times the U.S. military has claimed he is not a real person but an invented one, a fictional leader of a fictional state.

If the claims are indeed true this time, expect al Qaeda to laud its martyrs publicly. It will be a serious but not fatal blow to al Qaeda in Iraq. The al Qaeda franchise in Iraq has been in retreat for the last four years—ever since its founder Abu Musab al Zarqawi was killed on June 7, 2006 by an American air raid. What is so astonishing is not that al Qaeda in Iraq is now in retreat, but rather how close it came in 2005 and 2006 to pushing Iraq into a civil war and defeating the American intervention in Iraq with very little real popular support in the country and a leadership composed largely of foreigners like Zarqawi, a Jordanian, and al Masri, an Egyptian.

Start from the beginning. On September 11, 2001 there was no al Qaeda in Iraq and no connection between Saddam Hussein’s government and al Qaeda. Saddam had nothing to do with 9/11, despite what the Bush administration tried to make you believe. We invaded Iraq not because it had been a base for the most deadly attack on our country since 1814 when the British burned the White House. As Max Cleland, former U.S. Senator from Georgia and Vietnam veteran said “attacking Iraq after 9/11 was like attacking Mexico after Pearl Harbor.”

But al Qaeda was quick to see where Bush was going. Zarqawi moved into Iraq after he and the rest of al Qaeda’s network of terrorists were expelled from Afghanistan in late 2001. He worked carefully and successfully to prepare and build an infrastructure to attack the American occupation force once it overran Iraq in 2003—including networks of supporters in the Muslim diaspora in Europe and all over the Islamic world to funnel volunteers, many of them suicide bombers, into Iraq once the occupation began. In short, al Qaeda prepared for the occupation of Iraq far more effectively and efficiently than did the Pentagon.

On February 11, 2003, Osama bin Laden sent an open letter to the Iraqi people warning them that Bush was getting ready to attack their country. Bin Laden blamed the conspiracy on the Crusaders and Zionists who wanted to “install a stooge regime to follow its masters in Washington and Tel Aviv to pave the way for the establishment of Greater Israel.”

Within months of the occupation, al Qaeda in Iraq was assassinating senior Shia leaders and bombing Shia mosques to incite a Sunni-Shia civil war. It also moved rapidly to drive out of the country all those non-American players like the U.N. which would be crucial to post-invasion governance. The bombing of the U.N. headquarters on August 19, 2003 was an early indication of how carefully the terrorists had planned and prepared.

Then, al Qaeda overplayed its hand. Even by the tough standards of Iraq, Zarqawi was a brutal and sadistic murderer. Inside al Qaeda he was called “the stranger” for his extreme views. Attacking mosques and wedding parties, killing other insurgents and proclaiming a separate Sunni Arab state, the Islamic State of Iraq, he went too far and provoked a backlash. Bin Laden and Ayman Zawahiri tried to persuade Zarqawi not to go so far, but he did not listen. After his death, however, they lauded him as a great martyr for the jihad.

What he did do was buy them time. While America was focused on Iraq, bin Laden and Zawahiri rebuilt al Qaeda in Pakistan and staged a remarkable comeback in Afghanistan along with the Taliban. That disaster was what Barack Hussein Obama inherited from his predecessor a year ago. The Iraqi government’s announcement claimed bin Laden was communicating with al Masri and al Baghdadi directly—underscoring the fact that the al Qaeda core leadership is still very much alive and deadly, orchestrating a global jihad nine years after 9/11.

Al Qaeda always faced a difficult operating environment in Iraq. The majority of Iraqis are not Sunni Arabs and resent foreigners interfering in their country. If al Qaeda has been dealt another blow in Iraq this week that is an accomplishment, but probably not the end of the remarkable odyssey of al Qaeda in Iraq.