It's a nightmare scenario: Al Qaeda terrorists, funded by Usama bin Laden's millions and with access to Saddam Hussein's hidden stockpiles of chemical and biological weapons, unleash carnage that dwarfs even the fury of the Sept. 11 attacks.

In making his case for possible war with Iraq, President Bush warned such a day might come if America fails to act, but there is no known evidence of a link between Washington's chief villains.

The two men -- one married to religious extremism, the other a calculating secularist -- would make strange bedfellows, agreeing perhaps only on their hatred for the United States.

"Ideologically and logically, they cannot work together," Gen. Hamid Gul, the former chief of Pakistan's spy agency InterServices Intelligence, told The Associated Press. "Bin Laden and his men considered Saddam the killer of hundreds of Islamic militants," a reference to Saddam's relentless crackdowns on domestic political rivals, including Kurds and Shiites.

Pakistan, a longtime supporter of the hardline Taliban regime in Afghanistan, has a long history of monitoring bin Laden's comings and goings. Many Al Qaeda fighters, including perhaps bin Laden himself, are believed to have fled into the mountainous border region between the two countries after the U.S.-led war drove the Taliban from power in late 2001.

In his State of the Union address Tuesday, Bush used the alleged link between Saddam and Al Qaeda as a major argument in his push for a tough stance on Iraq.

"Evidence from intelligence sources, secret communications and statements by people now in custody reveal that Saddam Hussein aids and protects terrorists, including members of Al Qaida," the president said.

"Imagine those 19 hijackers with other weapons and other plans -- this time armed by Saddam. It would take one vial, one canister, one crate slipped into this country to bring a day of horror like none we have ever known," he added.

The president offered no new evidence, but said Secretary of State Colin Powell would present the U.S. case to the United Nations next week.

Bush's comments were dismissed by Iraqi Deputy Prime Minister Tariq Aziz.

"I absolutely deny that," Aziz told the British Broadcasting Corp. "Historically speaking, everybody in the region, everybody in the world knows Iraq has no connection with Al Qaeda. We are quite different people -- different in ideology, different in practice."

Certainly, an alliance between Saddam and bin Laden would have seemed impossible before Sept. 11.

In 1999, bin Laden was considering leaving Afghanistan amid U.S. pressure on the Taliban to kick him out in the wake of the Al Qaeda-linked bombings a year earlier of two U.S. embassies in Africa.

Going to Iraq was apparently never an option.

A Taliban commander told The Associated Press at the time that despite Saddam's battle with the United States, bin Laden would not relocate to Iraq because "he has differences with Saddam. He is not a good Muslim. Saddam does not care about Islam like Usama." The commander refused to be identified for fear of reprisal.

Indeed, Saddam's Baath party is just the sort of secular Arab government that the ultra-religious Al Qaeda organization would be likely to oppose. Bin Laden's beliefs sprung from the deeply conservative Wahhabi movement, which rejects smoking, drinking and socializing between men and women.

Baath socialism, by contrast, emerged in the 1950s as a mix of leftist economics, Arab nationalism and secular social policy, though Saddam has drawn on religion more and more since his defeat in the 1991 Gulf War.

Analysts caution that history means nothing in the shifting realities of the post-Sept. 11 world.

"On the face of it, their views of the role of religion in running an Arab society make them strange bedfellows, but that they could become united due to their sheer loathing of the United States -- it would be foolish to exclude such a possibility," said Warren Bass, a Middle East expert at the New York-based Council on Foreign Relations.

And while the evidence presented publicly by the Bush administration is not overwhelming, there are some signs that could point to an alliance of convenience between the two men.

There are also fears that a desperate Saddam might reach out to Al Qaeda if his regime appeared to be in peril.

In November, bin Laden re-emerged after months of silence in an audiotape sent to the Al-Jazeera television network.

Many counterterrorism experts suspect the Al Qaeda leader intentionally timed release of the tape to thrust himself into the dispute over the return of U.N. weapons inspectors to Iraq.

U.S. intelligence officials say some Al Qaeda members traveled through Iraq on their way home from the Afghan war, and a U.S. defense official said at least one senior operative, Abu Musab Zarqawi, went to Baghdad to seek hospital treatment before leaving for Syria.

In addition, a small Iraqi Kurdish group, Ansar al-Islam, is said to have sent some of its members to Afghanistan to train in Al Qaeda camps.

Finally, there were reports last year by Czech intelligence that Sept. 11 hijacker Mohamed Atta met in Prague with an Iraqi agent. But Czech authorities have since retracted the claim, and even Washington now says they no longer believe the meeting ever took place.