Early last month, Kyrgyzstan's president, Kurmanbek Bakiyev, went cap in hand to Moscow to ask for financial aid. To make his request more palatable, Bakiyev announced that he was demanding that the US close its airbase in Kyrgyzstan, which re-supplies Nato troops in neighbouring Afghanistan. Similarly, late last year, Iceland's government asked Russia to help bail out its banking system, while the Pakistani president, Asif Ali Zardari, visited China in the hope of securing an emergency infusion of cash.

Some observers cite these episodes as evidence of decline in America's international clout. But there's a larger point: so far – except for relatively small sums offered to the Kyrgyz – Russia and China haven't offered much help.

Amid much talk of a "post-American world", many observers see a shift from a US-dominated international order toward a multipolar system, in which countries like China, Russia, and several others compete for global leadership on a range of common challenges and risks.

More than five years ago, China's president, Hu Jintao, proclaimed that "the trend toward a multipolar world is irreversible and dominant". When Vladimir Putin complained during a conference in Munich last year that US unilateralism stoked conflict around the world, an offended Senator John McCain responded that confrontation was unnecessary in "today's multipolar world".

When Putin welcomed the Venezuelan president, Hugo Chávez to Russia last September, he observed that "Latin America is becoming a noticeable link in the chain of the multipolar world that is forming". Chávez agreed: "A multipolar world is becoming reality."

All of them have it wrong. US dominance is clearly on the wane, but a multipolar order implies that several emerging powers hold competing views about how the world should be run, and that they are prepared to act to advance their global agendas. That is not the case.

Instead, we are witnessing the birth of a non-polar order, in which America's chief competitors remain too busy with problems at home and in their immediate neighbourhoods to shoulder the heaviest international burdens. Not one of the emerging powers has even begun to use its growing political and economic clout to advance truly global ambitions – or to take on responsibilities that Washington can no longer afford.

Start with Russia. Despite its growing ties with Venezuela and efforts to co-ordinate energy policy with natural gas-rich countries in North Africa, the Kremlin has no aspirations to rebuild Soviet-scale influence in Latin America, Africa, or South-east Asia. Nor does it have Soviet-style ideological appeal. Instead, Russia's leaders are busy protecting Russian markets, banks, and companies from the worst effects of the global financial crisis, consolidating state control over domestic economic sectors, and extending their foreign-policy leverage across former Soviet territory.

China's need to satisfy its hunger for imported oil and other commodities has given it an international presence. But its influence is more commercial than political. China's leaders must devote their attention to a staggering array of pressing problems at home: averting an economic slowdown that could push millions out of work and into the streets, the fallout from rural land reform, and efforts to manage enormous environmental and public health problems.

India must hold its own in China's lengthening shadow. Facing elections next year, the ruling Congress party is spending the government's time and money on subsidies for consumers, wage hikes for state employees, and debt relief for farmers.

Brazil is similarly preoccupied, appearing to have no grander near-term aspirations than to promote stability in Latin America, manage the effects of the global financial crisis, and inspire others in the developing world.

In short, there is a vacuum of global leadership just at the moment when it is most badly needed. Barack Obama's attention is now concentrated on stimulating the anaemic US economy, crafting tax cuts, reforming energy and health-care policies, and restoring confidence in US financial institutions. The European Union continues its internal debate over how best to bail out its failing banks and industries, handle the fallout from EU and euro-zone expansion, and manage increasingly rocky relations with Russia.

Who, then, can take the lead on efforts to create a new global financial architecture that reflects the complexities of 21st-century commerce? Who can drive consensus on a multilateral response to climate change? Who will replace an obsolete non-proliferation regime, provide collective security in emerging international hotspots, and build momentum behind Middle East peace talks?

The international summit meeting in Washington in November 2008 underlined the problem. The world's richest countries (the G7) turned to the emerging powers within the G20 to help coordinate a response to the global financial slowdown. Difficult as it is for seven countries to agree on anything, imagine the challenge of building consensus among 20.

Consider the competing views within this group on democracy, transparency, the proper economic role of government, new rules of the road for financial markets and trade, and how best to ensure that the United Nations, International Monetary Fund, and the World Bank fairly reflect today's global balance of power.

For the next several years, when those in crisis turn to the US for help, they are increasingly likely to hear the word "no". And it is not at all clear that anyone else is willing and able to say yes.

In co-operation with Project Syndicate, 2009