AS CHINA'S power grows, we all know that its ambitions for regional influence are growing too. But it is not very clear how much influence China wants over its neighbours, and what kind of new regional order it wants to see.

And until we understand this better, it will be hard for China's neighbours in Asia to know how to respond to its ambitions.

China's aims are unclear because its leaders probably are not completely sure themselves what they want, and anyway will not say so. Until a couple of years ago, they followed Deng Xiaoping's precept of biding time and hiding its ambitions. Now that they are more assertive, they still will not spell out how they see China's role in Asia changing.

However, we can hazard some judgments to guide our thinking about how to deal with China over the coming years. First, it seems that China has no major territorial ambitions in Asia. This is not to say that China seeks no territorial changes at all.

There are the special case of Taiwan and China's peculiar "nine-dotted line" claim to the South China Sea, as well as a series of territorial disputes with some of its neighbours. But there is no evidence that China harbours wider ambitions to take control of the sovereign territory of any of its neighbours, the way hegemonic powers in the past have done.

It essentially accepts the territorial status quo in Asia today. This is important.

What China wants

SECOND, there is no evidence that China wants to change the basic political and economic fabric of Asia today. This is not surprising, because Asia today works very well indeed for China, and there is little for it to gain by changing it. This makes China very different from the old Soviet Union, for example, which during the Cold War aimed to change the world's political and economic system fundamentally. China today seems to have no such aims.

But this does not mean China does not want big and potentially very unsettling changes. Because although it seems to accept the territorial status quo, and wants to preserve the basic workings of the regional order, China wants to change its own role in that order very radically.

It wants to change who is in charge. Beijing wants to replace the United States as Asia's primary power and the region's undisputed leader. That means, among other things, minimising America's regional role.

No one should be surprised by this. Rising powers have always sought a bigger regional role for themselves, at the expense of the established powers.

This is perhaps especially true of China, for which regional leadership can be seen simply as restoring its traditional place at the apex of the Asian order, and redressing what it sees as two centuries of injustice and humiliation.

It would indeed be quite extraordinary if China, of all countries, did not seek regional leadership as it builds the world's biggest economy.

Seeing things differently

NONETHELESS, many people still doubt that China will challenge the US-led status quo. They believe that while Beijing might desire to take the lead in Asia, it will not run the risk of pushing Washington aside, because that would threaten the regional stability on which China's economic growth, and hence the survival of the Communist Party, depends.

That assumes that Beijing shares Washington's view that maintaining US leadership is the only way to keep Asia stable.

But in Beijing they see things differently. They think that Asia could be just as stable under their leadership, and that China's growth prospects would actually improve if US influence waned. And they seem to expect that this change in regional leadership will happen smoothly, because America will eventually realise that it has no alternative but to make way for China gracefully.

What kind of regional leadership does China want to exercise? There seems no reason to fear that China today aims for anything like the kind of harsh militarised hegemony that Japan tried to impose on Asia before 1945.

It is more likely to aspire to maintain the less intrusive, and less expensive, kind of regional leadership that America has exercised for the past 40 years. But even if Beijing were content to lead Asia with a light hand, this would still be very hard for its neighbours to accept.

Why? Because China is not the US. America is far away from Asia, which makes it less intimidating than China, and the "soft power" of its values and institutions makes it easier to trust. Since Richard Nixon met Mao Zedong in 1972, US primacy in Asia has been essentially uncontested but Chinese primacy would be different.

Its neighbours fear that Beijing would abuse its power if it acquired unfettered regional leadership, so they would resist China's bid to take America's place. And acting together, led by powerful countries like Japan, India, Russia and Indonesia, they have the means to do so, especially with US support.

China's leaders, and ultimately the Chinese people, therefore face a painful reality.

Some alternatives

CHINA will probably never be accepted as the uncontested leader of Asia the way America has been. And no matter how strong it grows, it will not be able to impose its leadership on its unwilling neighbours, or exclude America from playing a major role in Asia. In short, China is not going to be able to get what it wants.

This means we have to ask another question: not what China wants, but what it can sensibly expect to get and what it might be willing to accept.

Is Beijing willing to scale back its ambitions for regional leadership in order to avoid escalating strategic rivalry with its neighbours? Will it accept America remaining a major power in Asia, strong enough to balance China's power and limit its influence?

Or is China so determined to take over as Asia's primary power that it would accept the huge costs and risks of open-ended strategic competition against both its Asian neighbours and the US?

That depends not just on how clearly Beijing sees the long-term balance of power relative to its potential adversaries, but also on how it sees the alternatives to primacy. If the Chinese think the only alternative to insisting on their own primacy in Asia is to continue indefinitely to accept the old status quo - with means their subordination to America - then China will most probably push ahead into a new Cold War.

Ideally, a shared primacy

BUT that is not the only option.

China would be much more likely to accept an outcome offering significantly more regional influence than it has had before, even if much less than the primacy it clearly wants. In other words, China might settle for being accorded an equal place in a new, collective, regional leadership system.

It would certainly make more sense for them. An equal role in the collective leadership of a stable Asia is much better for China than a terribly costly, and ultimately futile, bid for supremacy.

But the Chinese will only choose this option if they can be persuaded that it is available. And that depends on the rest of us, and especially on America. The more Washington continues to insist that American primacy is the only basis it is prepared to contemplate for Asia's future, the more Beijing will insist on replacing American primacy with its own.

So the hope that China will make sensible choices depends partly on America. Washington needs to understand that, in future, the US-led status quo cannot be maintained in Asia against China's will, any more than China can impose primacy in the face of America's power.

For both powers, and for the rest if us in Asia, cautious accommodation of one another's ambitions offers a much better future than the reckless pursuit of primacy by both sides, which is where we seem to be heading today.

The writer is professor of strategic studies at Australian National University and a visiting fellow at the Lowy Institute.

By Invitation features leading thinkers and writers from the region and Singapore.