17 January 2011 Last updated at 19:00 ET

Hu Jintao in Washington: What China and the US want

As Chinese leader Hu Jintao travels to the United States on a state visit, the BBC looks at what each country wants from the other.

Michael Bristow, BBC News, Beijing

It is difficult to be clear about what China wants from President Hu Jintao's visit to the United States - officials here do not want to give details.

At a news briefing organised to discuss the trip, Cui Tiankai, a vice-foreign minister, talked in vague terms about a "sound and steady development of the bilateral relationship".

But he gave few specifics, and dodged the question when asked to give some.

There are some obvious talking points that will probably come up on the trip, including the value of China's currency and the trade surplus it enjoys with the US.

Beijing has long wanted Washington to stop selling arms to Taiwan, a self-governing island that China considers part of its territory. It would be no surprise if China brought the subject up again.

There is also a larger question that both countries need to resolve.

Beijing and Washington will have to work out how to manage their changing relationship.

China might currently be the junior partner but, as it grows stronger, it will want a greater say in how the world is run, particularly in the Asia-Pacific region.

"The growing strength of China and its standing in the world is a reality," Mr Cui said at last week's news briefing.

He added: "While we respect and understand US interests, we also hope the US respects and understands China's position."

Over the last few years, Chinese leaders, aware of the country's growing power, appear to have become more assertive.

They have, for example, turned up the rhetoric when talking about the country's territorial claims in the seas around the country.

But China will not want too much change too quickly. That might lead its neighbours - and the US - to wonder about its ultimate aims.

To soothe fears, Beijing constantly repeats that its rise is peaceful and non-threatening.

"There is no issue of conflict between [China and the US]," said Mr Cui.

That might be the hope in Beijing, but it will not be easy for Presidents Hu Jintao and Barack Obama to find a way to make that a permanent reality.

Paul Adams, BBC News, Washington

At least one man who ought to know thinks this visit is a very big deal.

"The most important top-level United States-China encounter since Deng Xiaoping's historic trip more than 30 years ago," was how Zbigniew Brzezinski described President Hu Jintao's visit in a New York Times column earlier this month.

Mr Brzezinski was Jimmy Carter's national security adviser at the time of Mr Deng's visit, and he argues that this encounter should go beyond "boilerplate professions of mutual esteem" and properly define this 21st-Century relationship.

It is, perhaps, a tall order. The past year has, by general consent, been a difficult one for US-China relations. While it is very easy to define the obstacles to a mutually beneficial relationship (trade, currency, military rivalry, etc), it's not so easy to say where their interests overlap.

Treasury Secretary Timothy Geithner had a good stab during a speech at Johns Hopkins University last week.

The economic relationship, he said "provides tremendous benefits to both our nations". Despite competition, he added, "our economic strengths are largely complementary".

He agreed that the benefits of the relationship were hard to capture in a single statistic, but suggested the US was "on track to export more than $100bn (£63bn) of goods and services to China" in 2011, and that hundreds of thousands of American jobs were being supported as a result.

The figures were impressive and ran counter to the image, entertained by many Americans, that it's all one-way traffic - in the opposite direction.

Last year's mid-term election campaign was more than usually marked by populist rhetoric, as would-be members of Congress accused each other of supporting moves that have shifted jobs to China.

If, as seems likely, Mr Hu uses his visit to sign a number of contracts beneficial to US companies, it will help Mr Obama put a positive gloss on the relationship.

But Mr Geithner peppered his generally upbeat talk with references to America's traditional concerns over exchange rates and capital flows. Keeping the Chinese currency substantially undervalued, he said, was "not a tenable policy for China or the world economy".

Of course, he knows only too well that China has its own views on what constitutes a tenable economic policy, and America's still faltering efforts to dig itself out of a financial crisis brought about by a prolonged debt binge do not exactly place Washington on the moral high ground.

As if all that weren't complicated enough, differences over human rights, policy towards North Korea and Iran, as well as China's growing military power, all make for a complex web of interlocking issues - with plenty of scope for discord.

In her own speech ahead of Mr Hu's visit, Secretary of State Hillary Clinton said the US would "continue to speak out and press China when it censors bloggers and imprisons activists".

She also said she wanted Beijing to send "an unequivocal message" that North Korea's recent actions, including its November artillery attack on a South Korean island, were "unacceptable".

Mr Obama's national security adviser, Tom Donilon, says the two leaders will focus on "four baskets": the overall US-China relationship, security and political issues, economic issues and human rights.

The approach suggests a desire to keep the baskets separate. That is probably essential if this visit is to live up to Mr Brzezinski's lofty expectations.