We tend to assume that power, like nature, abhors a vacuum. In the history of world politics, it seems, someone is always bidding for hegemony. Today it is the United States; a century ago it was Britain. Before that, it was the French, the Spaniards and so on. The 19th-century German historian Leopold von Ranke, doyen of the study of statecraft, portrayed modern European history as an incessant struggle for mastery, in which a balance of power was possible only through recurrent conflict.

Power, in other words, is not a natural monopoly; the struggle for mastery is both perennial and universal. The"unipolarity" identified by commentators following the Soviet collapse cannot last much longer, for the simple reason that history hates a hyperpower. Sooner or later, challengers will arise, and back we must go to a multipolar, multipower world.

But what if this view is wrong? What if the world is heading for a period when there is no hegemon? What if, instead of a balance of power, there is an absence of power? Such a situation is not unknown in history. Though the chroniclers of the past have long been preoccupied with the achievements of great powers -- whether civilizations, empires or nation states -- they have not wholly overlooked eras when power has receded. Unfortunately, the world's experience with power vacuums is hardly encouraging. Anyone who dislikes U.S. hegemony should bear in mind that, instead of a multipolar world of competing great powers, a world with no hegemon at all may be the real alternative to it. This could turn out to mean a new Dark Age of waning empires and religious fanaticism; of endemic rapine in the world's no-go zones; of economic stagnation and a retreat by civilization into a few fortified enclaves.

Why might a power vacuum arise early in the 21st century? The reasons are not especially hard to imagine.

• The clay feet of the colossus. The U.S. suffers from at least three structural deficits that will limit the effectiveness and duration of its crypto-imperial role in the world. The first is the nation's growing dependence on foreign capital to finance excessive private and public consumption. It is difficult to recall any empire that has long endured after becoming so dependent on lending from abroad. The second deficit relates to manpower: The U.S. is a net importer of people and cannot therefore underpin its hegemonic aspirations with real colonization; at the same time, its relatively small volunteer army is already spread very thin as a result of recent military interventions in Afghanistan and Iraq. Finally, the U.S. is afflicted by what is best called an attention deficit. Its republican institutions make it difficult to establish a consensus for long-term"nation-building" projects.

•"Old Europe" grows older. Those who dream that the European Union might become a counterweight to the U.S. should continue slumbering. Impressive though the EU's enlargement has been, the reality is that demography likely condemns it to decline in international influence. With fertility rates dropping and life expectancies rising, European societies may, within less than 50 years, display median ages in the upper 40s. Indeed,"Old Europe" will soon be truly old. By 2050, one in every three Italians, Spaniards and Greeks will be 65 or over, even allowing for immigration. Europeans therefore face an agonizing choice between"Americanizing" their economies, i.e., opening their borders to much more immigration, with the cultural changes that would entail, or transforming their union into a fortified retirement community.

• China's coming economic crisis. Optimistic observers of China insist that the economic miracle of the past decade will not fade -- that growth will continue at such a pace that within three or four decades China's GDP will surpass that of the U.S. Yet it is far from clear that the normal rules that apply to emerging markets have been suspended for Beijing's benefit. First, a fundamental incompatibility exists between the free-market economy, based inevitably on private property and the rule of law, and the persistence of the Communist monopoly on power, which breeds rent-seeking and corruption, and impedes the creation of transparent institutions. As usual in"Asian tiger" economies, production is running far ahead of domestic consumption -- thus making the economy heavily dependent on exports. No one knows the full extent of the problems in the Chinese domestic banking sector. Western banks that are buying up bad debts with a view to establishing themselves in China must remember that this strategy was tried a century ago, in the era of the Open Door policy, when American and European firms rushed into China only to see their investments vanish in the smoke of war and revolution. Then, as now, hopes for China's development ran euphorically high, especially in the U.S. But those hopes were disappointed, and could be disappointed again. A Chinese currency or banking crisis could have earth-shaking ramifications, especially when foreign investors realize the difficulty of repatriating assets held in China.

• The fragmentation of Islamic civilization. With birthrates in Muslim societies more than double the European average, Islamic countries are bound to put pressure on Europe and the U.S. in the years ahead. If, as is forecast, the population of Yemen will exceed that of Russia by 2050, there must be either dramatic improvements in the Middle East's economic performance or substantial emigration from the Arab world to senescent Europe. Yet the subtle colonization of Europe's cities by Muslims does not necessarily portend the advent of a new and menacing"Eurabia." In fact, the Muslim world is as divided as it has ever been. This division is not merely between Sunni and Shiite. It is also between those seeking a peaceful modus vivendi with the West (embodied in Turkey's desire to join the EU) and those drawn to the Islamic Bolshevism of the likes of Osama bin Laden. Opinion polls from Morocco to Pakistan suggest high levels of anti-American sentiment, but not unanimity. In Europe, only a minority expresses overt sympathy for terrorist organizations; most young Muslims in England clearly prefer assimilation to jihad. We are a long way from a bipolar clash of civilizations, much less the rise of a new caliphate that might pose a geopolitical threat to the U.S.

In short, each of the obvious 21st-century hegemons -- the U.S., Europe, China -- seems to contain within it the seeds of decline; while Islam remains a diffuse force in world politics, lacking the resources of a superpower....