EVEN if American and Iraqi forces are able to eliminate Al Qaeda in Iraq, there are still three worrisome possibilities of new forms of fighting that could divide Iraq and deny the United States any form of “victory.”

One is that the Sunni tribes and militias that have been cooperating with the Americans could turn against the central government. The second is that the struggle among Arabs, Kurds, Turkmen and other ethnic groups to control territory in the north could lead to fighting in Kirkuk, Mosul or other areas.

The third risk — and one that is now all too real — is that the political struggle between the dominant Shiite parties could become an armed conflict.

Fighting is now occurring in southern Iraq and parts of Baghdad between the Mahdi Army, which is under the control of the populist cleric Moktada al-Sadr, and a coalition of forces led by Prime Minister Nuri Kamal al-Maliki’s Dawa Party and the Islamic Supreme Council of Iraq, a powerful party led by a Maliki ally, Abdul Aziz al-Hakim. This latter coalition has de facto control of much of the Iraqi security forces, and Mr. Hakim’s group has its own militia, called the Badr Organization.

Much of the reporting on this fighting in Basra and Baghdad — which was initiated by the Iraqi government — assumes that Mr. Sadr and his militia are the bad guys who are out to spoil the peace, and that the government forces are the legitimate side trying to bring order. This is a dangerous oversimplification, and one that the United States needs to be far more careful about endorsing.

There is no question that many elements of the Mahdi Army have been guilty of sectarian cleansing, that the Sadr movement is hostile to the United States, that some of its extremists have continued acts of violence in spite of the cease-fire Mr. Sadr declared last summer, and that some of these rogue elements have ties to Iran. No one should romanticize the Sadr movement, understate the risks it presents or ignore the violent radicals in the Mahdi Army.

But it is equally important not to romanticize Mr. Maliki, the Dawa Party or the Islamic Supreme Council. The current fighting, which the government portrays as a crackdown on criminality, is better seen as a power grab, an effort by Mr. Maliki and the most powerful Shiite political parties to establish their authority over Basra and the parts of Baghdad that have eluded their grasp.

Moreover, Mr. Maliki’s gamble has already dragged American forces part-way into the fight, including airstrikes in Basra. Striking at violent, rogue elements in the Mahdi Army is one thing, but engaging the entire Sadr movement is quite another. The official cease-fire that has kept the mainstream Mahdi Army from engaging government and United States forces may well be rescinded if the government’s assault continues.

This looming power struggle was all too clear when I was in Iraq last month. The Supreme Council was the power behind the Shiite governorates in the south and was steadily expanding its influence over the Iraqi police. It was clearly positioning itself to counter Mr. Sadr’s popular support and preparing for the provincial elections scheduled for Oct. 1.

American military and civilian officials were candid in telling me that the governors and other local officials installed by the central government in Basra and elsewhere in southern Iraq had no popular base. If open local and provincial elections were held, they said, Dawa and the Islamic Supreme Council were likely to be routed because they were seen as having failed to bring development and government services.

There was no real debate over how bad the overall governance of the south was at the provincial level, how little money the region was getting from Baghdad, and how poor government-related services were, even in Shiite areas. Incompetence and corruption are not sectarian. An ABC News poll released this month showed that only two-thirds of the Shiite population in Basra had a favorable opinion of the central government, down from three-quarters last summer, and that only 14 percent of all residents felt they could move about safely.

The American officials I met with differed in their views of the size of Mr. Sadr’s populist base around Basra, but most felt that Mr. Sadr still had a broad base of support in Baghdad — something indicated by the huge rallies on his behalf in the capital last week.

As I traveled through southern Iraq, many people I spoke to were worried about how the October elections would play out. The first problem is that there are no real indigenous political parties operating with local leaders. The second is the framework, which is still undecided. If the election follows the model of the 2005 vote, Iraqis will vote for long lists of candidates from the main parties (confronting many unfamiliar names) and there will be no allowance for the direct election of members of the Parliament who would represent a given area or district. Optimists hope that local leaders and parties will emerge before the election; realists foresee an uncertain mess.

There were also differences of opinion over Mr. Sadr’s cease-fire. Was he simply waiting out the American-Iraqi effort to defeat Al Qaeda before allowing his army to become active again? Or was he repositioning himself for a more normal political life? Most likely, he is doing both. He may be as confused by the uncertain nature of Iraqi politics as everyone else, and he may be dealing with a movement so fractured and diverse that effective control is nearly impossible.

In any event, it is clear that Basra has become a special case. Since the American-led invasion, it had been under the protection of the British, who opted for a strategy of not-so-benign neglect. Thus the power struggle in the city — Iraq’s main port — differs sharply from that in the other Shiite areas. Basra was essentially divided up among Shiite party mafias, each of which had its own form of extortion and corruption. They sometimes fight and feud, and there are reasons to call them criminal gangs, but they have established crude modus vivendi.

Basra also feels the influence of Iran far more than the other Shiite governorates. Iran’s religious paramilitary force, Al Quds, has been an equal-opportunity supplier of weapons and money to all the Shiite militias, effectively ensuring that it will support the winner, regardless of who the winner turns out to be.

There are good reasons for the central government to reassert control of Basra. It is not peaceful. It is the key to Iraq’s oil exports. Gang rule is no substitute for legitimate government. But given the timing and tactics, it is far from clear that this offensive is meant to serve the nation’s interest as opposed to those of the Islamic Supreme Council and Dawa.

How will it affect America? If the fighting sets off a broad, lasting, violent power struggle between Shiite factions, most of the security gains of the last year could be lost and our military role broadened. There is also no guarantee that a victory by Dawa and the Islamic Supreme Council will serve the cause of political accommodation or lead to fair elections and the creation of legitimate local and provincial governments. Such an outcome, in fact, might favor a Dawa and Islamic Supreme Council “Iraqracy,” not democracy.

* By ANTHONY H. CORDESMAN (Washington, March 30,2008)

Anthony H. Cordesman is a fellow at the Center for Strategic and International Studies.