No one should be disappointed by the outcome of the US-China summit in Washington last month, because nothing much was expected from it. For Hu, it was a 'legacy' visit, his swansong as the head of the world's most populous and potentially most powerful nation before stepping down as the leader of the Communist Party of China in 2012. The Obama White House obliged by allowing him to make the first state visit to the White House by a Chinese leader since Jiang Jemin in 1997.

This, too, is not surprising. During the past year China's image and soft power has taken a battering, especially in the Asia Pacific, where it rekindled mistrust by asserting claims over South China Sea, refusing to condemn North Korea for its aggressive tactics towards the South and restricting exports of rare earth elements. The US has gained considerable mileage out of these Chinese missteps, despite the Chinese snub to Obama at the Copenhagen climate talks in December 2009, and Beijing's harsh condemnation of the $6. 4 billion US arms sale to Taiwan and the Dalai Lama's visit to the White House.

As fears of China are rekindled in Asia by Beijing's own assertiveness, there is a new recognition of America's role there as the provider of security. The Obama administration could thus afford to look generous and reward China for taking some conciliatory steps in the months leading to the Hu visit - like letting its currency appreciate a bit, and allowing a visit to China by defense secretary Robert Gates.

But for those who see the US and China as leaders of the 21st century global order, the summit holds an important lesson: while the unipolar moment in international relations is over, it will not be replaced by a China-US duopoly, at least an effective one, that addresses the global challenges of our time.

No one can deny the power shift, although the US president did try. At their joint press conference, Obama told the visitor (and more to the American people perhaps ): "we have to remind ourselves that the United States' economy is still three times larger than China's despite having one-quarter of the population". But just over a decade ago, in 2001, the US economy was more than 7 times larger than China's.

The Hu visit made two things very clear. First, America's domestic politics would prevent the two sides from developing the trust needed for effective cooperation. Second, issues in the bilateral relationship take priority over tending to the problems of the world at large.

The thrust of the entire visit was on bilateral issues, America's trade deficit, China's currency manipulations and, of course, China's abysmal human rights record. After initially avoiding a question on the subject (by citing a translation glitch) at his joint press conference with Obama, Hu replied to a follow-up that "China is always committed to the protection and promotion of human rights", citing the "enormous progress, recognised widely in the world" it has made over the issue. But he also asked "to take into account the different and national circumstances when it comes to the universal value of human rights".

Over global governance issues, Hu mentioned at the press conference China's support for the G20 to play "a bigger role in international economic and financial affairs, " and to "work with the United States and other countries to effectively address global challenges" such as climate change and terrorism.

By all indications, the US is coming to terms with the end of its G-1 world, although it is still impolite to mention the 'D" word (decline) in Washington. While Secretary of State Hillary Clinton did talk about "the new American moment" in international affairs, it was a call for sharing the burden with others, including emerging powers (China being one but not the only one) of them. It also called for working through global and regional institutions to advance US interests.

When the US replaced Britain as the global hegemon after the end of World War II, it was not shy of accepting international obligations and making sacrifices. Why is not China following the US path to global leadership, albeit a shared one with the US?
When the US, under the Bush administration, was riding high in the unipolar moment, China was (secretly) thrilled to be counted as the main challenger to US dominance. Many Chinese still do, but being a challenger is not the same as being a leader.

Some blame it on Deng Xiaoping, China's late paramount leader, who is supposed to have warned against China becoming a leader in the world. But this is an urban myth. Deng was more nuanced and qualified, and China today is far more powerful than during Deng's time.

The Chinese are scared of global leadership because they it see it as a ploy to force them into prematurely accepting responsibilities that will undercut their 'peaceful rise'. And the Chinese have dismissed the idea of a joint leadership with the US, not because they do not relish the status that comes with it, but because it calls for sacrifices that they are unwilling to make, like accepting significant binding cuts in their carbon emissions.

If the burden of domestic politics and bilateral mistrust limits the ability of the US and China to jointly manage global issues, it leaves room for others - India, Europe, Canada and other G-20 nations - to step in and have their say. For them, this might be the good news from the summit.

The writer is professor of International Relations at American University, Washington, D. C.