For supporters of democracy, there is nothing more exciting or memorable than the fall of another dictator. The construction of a new political system, however, is a much more ambiguous process. The French still commemorate the storming of the Bastille, but the consolidation of democracy afterward took decades. Russian democrats at one point celebrated August 1991 as the month Soviet communism collapsed, but they stopped having parties later in the decade, when democracy's arrival still seemed far away. Navigating the gap between the fall of the old order and the formation of the new order is always difficult; it's especially dangerous when extremist movements and ideologies are added to the mix.

Iraq has it all: ethnic and religious divides, foreign troops, and returning exiles and revolutionaries ready to step in with an alternative vision for how to organize Iraqi state and society when those who first take power fail. Although Germany, Japan and France in 1945, or Haiti and the Balkans in the 1990s, have become the analogous regime changes of choice for many Western analysts, we would do well to add France in 1789, Russia in 1917 and 1991, Iran in 1979 or Afghanistan in the early 1990s as other historical metaphors that may help us understand Iraq today. These revolutionary situations shared several characteristics after the fall of the old order.

First, the collapse of the old regime left a vacuum of state power. The anarchy, looting and interruption of state services that we see in Iraq are predictable consequences of regime change. Second, after the fall of the dictator, expectations about "life after the dictator" exploded. People who have been oppressed for decades want to benefit from the new order immediately. The urgent and angry questions last week from Ahmed Chalabi, the Iraqi National Congress leader now back in Iraq, about why the Americans have not provided more relief faster is typical. The first leaders after the departure of the king in France, the czar in Russia or the communists in Eastern Europe knew Chalabi's situation well. Paradoxically, society's expectations inflate at precisely the same moment when the state is least prepared to meet them. Third, the coalition that opposed the dictatorship dissolved. While the dictator was still in power, this united front embraced one ideology of opposition -- "anti-king," "anti-czar," "anti-shah" or "anti-communist." In doing so, these coalitions consisted of economic, political, ethnic and religious forces with radically different visions for their country after regime change. Unity ended after the dictator fell. In Russia, Bolsheviks and liberals in 1917 and nationalists and democrats in 1991 went their separate ways. In Iran in 1979, Islamic leftists, liberals and militant clerics celebrated their shared goal of removing the shah. Just a few years after the collapse of the old order, many of the coalition partners who brought down the shah were out of power or in jail. Soon after the Soviet puppet regime in Afghanistan fell, the anti-Soviet coalition forces were killing each other.

The Iraqi opposition today consists of exiled liberals and generals, Kurdish nationalists, Shiite and Sunni clerics, Islamic fundamentalists, a smattering of monarchists and the unknown local leaders throughout the country who have quietly provided comfort to opponents and passive resistance to Saddam Hussein's totalitarian regime. From other regime changes, we should assume that this united front against Hussein will no longer be united after Hussein. The combination of a weak state, soaring expectations in society and factional fighting in the anti-authoritarian coalition gives rise to two dangerous "solutions." One is restoration. Living in anarchy, people want order. Who can provide order most quickly? Those who previously provided order. How can order be provided most quickly? By deploying the same methods used before. For both American officials governing Iraq and the Iraqi people, the temptation to settle for a new regime led by new leaders with autocratic proclivities grafted onto old state structures from Hussein's regime will be great.

But there is another, more sinister solution that can also gain appeal: the victory of the extremists. The end of dictatorship is a euphoric but ephemeral moment. When the new, interim government does not meet popular expectations, the radicals offer up an alternative vision to construct a new political (and often social) order. It is amazing and frightening how often they win. In February 1917 the end of Russian czarism seemed to create propitious conditions for constitutional democracy. Less than a year later, the Bolsheviks had seized power. In 1979 the first provisional government in Iran contained many prominent leftist intellectuals and even some liberals. No one today, however, remembers Mehdi Bazargan or Abol Hassan Bani-Sadr, while everyone knows the name of Ayatollah Ruhollah Khomeini, the radical cleric who pushed these others aside to dictate his vision for Iran. The Taliban seized control in Afghanistan to end the years of anarchy after the collapse of the old order there.

In Iraq, this threat from revolutionaries -- that is, the terrorist wing of Islamic fundamentalism inspired by Osama bin Laden -- is now latent and below the radar screen, but real. For devotees of this world perspective, Iraq offers a ripe opportunity. Not only is the old state gone and expectations high, but the only authority in the country is, in their revolutionary discourse, an imperial occupying force of infidels. Vladimir Lenin and Khomeini would have drooled over such propitious conditions for revolution.

The third path between restoration and revolution is a long and bumpy one. Liberal, moderate grass-roots movements from below always take more time to emerge and consolidate than the autocratic forces of either restoration or revolution. To succeed in Iraq, they will need their U.S. allies for the long haul. Premature departure guarantees thugs in power at best and Osama bin Laden supporters at worst.

The writer is a Hoover fellow and professor of political science at Stanford University and a senior associate at the Carnegie Endowment for International Peace.