As we watch the televised images of a defiant Saddam Hussein and of U.S. tanks stuck in the mud on the road to Baghdad, we might want to keep in mind this sobering thought: The military battle now raging in Iraq is merely a small slice of an even larger, longer and more unpredictable political war.

Several very different campaigns are unfolding within the framework of President Bush's worldwide war on terrorism. Alongside a series of military operations, from Afghanistan to Iraq, there is a diplomatic front, an economic front, a propaganda front and a homeland security front. The most fateful war of all may be the one that is being waged for the hearts and minds of 250 million Arabs. After all, it is the Arab world that has supplied both the ideologists and the foot soldiers in the most formidable challenge to the United States since communism collapsed.

The risk that the United States could win a military victory in Iraq yet lose the broader political war was driven home to me during a reporting tour to the Middle East and Europe just before American missiles began falling on Baghdad. My travels took me from Saudi Arabia, the country of origin for 15 of the 18 hijackers involved in the 9/11 attacks, to Qatar, home of both the U.S. Central Command and the al-Jazeera television network, to NATO headquarters in Brussels and, finally, to Serbia, the target of a series of U.S. military interventions in the Balkans in the '90s, culminating in the 1999 Kosovo war.

Everywhere I went, people (including some U.S. soldiers and diplomats, speaking privately) expanded on much the same theme: Never before in history has there been a country as powerful as the United States -- militarily, economically, politically. But American power has also spawned fear of American dominance, which can take the form of outright delight whenever the world's sole superpower suffers a setback. "America has become a bully on a rampage," a prominent Saudi lawyer whose degree comes from an Ivy League university, told me in Riyadh. "It's a comment on how dismal we feel that we applaud anyone who puts up resistance to the imperial American project, whether it is Saddam Hussein or Kim Jong Il."

The lawyer went on to say that he did not know which to fear more -- an American triumph in Iraq or a defeat. Too easy a victory, he asserted, would encourage conservatives in the United States to take on new "imperial projects": Iran, North Korea, possibly Saudi Arabia itself. But a prolonged, bloody campaign would inflame supporters of Saudi-born terrorist leader Osama bin Laden.

Militarily, American power is so overwhelming that nobody will engage us on our own terms. Instead, America's enemies look for points of vulnerability. The catastrophic terrorism pioneered by bin Laden -- using civilian planes as missiles against the symbols of American economic and military power -- is one example of such "asymmetric warfare." Another is Hussein's decision to resort to guerrilla tactics to slow the U.S. advance in Iraq, from the arming of paramilitary groups to phony surrenders to yesterday's suicide car bombing that killed four U.S. soldiers lured by the driver's request for help. While we denounce such tactics, many in the Arab world see them as a legitimate response by the weak to the strong.

Bush administration officials are acutely aware of the importance of winning Arab hearts and minds, which is why they have imposed restrictive rules of engagement on U.S. troops. From the American point of view, the manner in which victory is achieved -- and how it is perceived in the Arab world -- is almost as important as victory itself. That means sparing civilian infrastructure where possible and hitting only "regime targets." It would be a simple matter to eliminate Iraqi resistance by flattening Baghdad or Basra. Indeed, some armchair strategists are calling for the U.S. military to stop fighting with "one hand behind its back." But that would defeat the war's larger political purpose, which is to convince Iraqis that the American invaders are "liberators, not occupiers."

Convincing Arab TV viewers that this is a humanitarian war may be mission impossible. War is undiscriminating by its very nature, particularly when pro-Hussein militiamen are interspersed with the civilian population. Civilians always get hurt, even in an age of precision targeting, as happened Wednesday and Friday when errant bombs fell on Baghdad marketplaces, killing dozens of civilians. Responsibility for the bombs has not been fixed, but in the Arab world, America is getting the blame. Before the global information age, such occurrences would have been isolated tragedies. These days, the images are transmitted all over the world instantaneously, magnifying their impact many times over and fueling already strong anti-American sentiments.

Sometimes, the same image can mean entirely different things to different audiences. When American viewers saw news footage of U.S. missiles raining down on Baghdad, they largely accepted the official Pentagon explanation that the destroyed buildings were all associated with Hussein's oppressive regime. Arab viewers tuning into the satellite television station al-Jazeera were given an impression of a city in flames, and of indiscriminate death and destruction.

When I visited al-Jazeera's newsroom in Qatar, the editor-in-chief, Ibrahim Hilal, made it clear that he would focus extensive attention on the suffering of Iraqi civilians. He predicted that as many as 100,000 Iraqi soldiers and civilians would be killed in the war, and half a million wounded. "Emotions are the most important part of the story," he told me. "Our job is to show the human side of the war." The Bush administration can't seem to make up its mind about al-Jazeera -- on the one hand, denouncing it for bias and sensationalism; on the other hand, trying to woo it by providing access and exclusive interviews with Secretary of State Colin Powell and other officials. An embedded al-Jazeera reporter is even traveling with the U.S. Marines.

Virtually everybody I talked to, including U.S. diplomats, said that the Bush administration has failed dismally in its ongoing public diplomacy efforts aimed at the Arab world. The State Department's "shared values" campaign -- which consisted of buying air time on Arab TV stations showcasing the lives of Arab Americans -- was an expensive flop. Many countries refused to air the ads, which they described as propaganda. According to the Zogby International polling firm, the proportion of Saudis with an "unfavorable opinion" of America has climbed from 87 percent to 97 percent over the past year. Few Saudis believe that the United States has invaded Iraq to install democracy there, so they conclude that there must be some other explanation, such as grabbing the country's oil wealth or helping Israel. "How can you talk of democracy in Iraq when you were in cahoots with Saddam a few years ago?" asked Khaled Maeena, editor of Arab News, an English-language newspaper based in Jiddah. "It's hypocrisy."

It is hard to overstate how much Arab attitudes toward America have been colored by the Israeli-Palestinian dispute. Saturation coverage of Palestinian suffering by al-Jazeera and other pan-Arab TV stations has fed a sense of grievance against Washington, widely seen as Israel's principal patron. "U.S. policies are not helping us at all," said Mishary Nuaim, chair of the political science department at Riyadh University, who regards himself as pro-American. "The U.S.-Israeli connection is enabling terrorist organizations to steal the show."

Viewed from the Saudi perspective, the precedent of the first Persian Gulf War is not encouraging. Even though that war appeared to end with a clear-cut American victory, it also set in motion a chain of threatening events that was impossible to predict at the time. The most ominous, in retrospect, was the boost the war gave to Islamic extremism in Saudi Arabia itself. Bin Laden used the U.S. military presence in "the land of Mecca and Medina" as a pretext for declaring jihad against America and the Saudi royal family.

It is possible, of course, that victory over Iraq will demoralize America's enemies, boost the cause of freedom throughout the Middle East and undermine the nexus between rogue states and international terrorism, as President Bush fervently hopes. But it could also lead to a surge in terrorism and anti-Americanism, further rupture a system of alliances dating back to World War II and trap America in a Vietnam-like quagmire. Given America's frayed relations with many of its own allies, winning the peace is likely to prove more challenging than winning the war. "I am not worried about the military side of the operation," a U.S. general told me before the war began. "I am worried by what happens afterward."

I got a chance to see what might happen afterward when I was diverted to Belgrade to report on the assassination of the Serbian prime minister, Zoran Djindjic. With its extremely complicated ethnic makeup, Yugoslavia provides a template for the kind of problems Iraq is likely to face after Hussein's overthrow. Iraq, like Yugoslavia, is a largely artificial product of the 1919 Treaty of Versailles -- a hodgepodge of different faiths, tribes and ethnic groups, including Sunnis and Shiites, Kurds and Turkomen. The Yugoslav experience suggests that, in the absence of a strong central authority maintaining some kind of balance between the rival ethnic groups, the whole edifice could come crashing down. Providing such authority in Iraq could keep the United States busy for many years.

After a decade of violent upheavals and foreign interventions, life is now getting a little better for the people of the Balkans. Peace has returned to most parts of the former Yugoslavia. Economic activity is picking up from catastrophically low levels. On the other hand, many people are disillusioned with politics. Djindjic's murder showed that it takes a lot more than a free election to root out the corruption and organized crime associated with the collapse of a one-party state. In Belgrade, there is still great resentment against the United States for the 11-week bombing campaign of 1999, even though it led to the overthrow of a brutal dictator 18 months later.

By invading Iraq, the United States is assuming some responsibility for the problems of that country, just as it did when it first sent troops into the Balkans in 1995 to enforce the Dayton Peace Agreement on Bosnia. At the time, President Clinton announced a cast-iron "exit strategy" under which the troops would be leaving within a year. Seven and a half years later, the troops are still there. Michael Dobbs covers foreign policy for The Washington Pos. He reported from Iraq during the Iran-Iraq war in the 1980s.

Images of Iraqi civilian casualties fuel protests here and abroad; al-Jazeera vows to show "the human side of war."