In Monday's presidential debate on foreign policy, President Obama and Mitt Romney will spar over China, covering everything from free trade to cyberattacks. But another topic — one that might not come up — is of growing concern: tensions in the waters off China itself.

This year, China has had run-ins with two U.S. allies — Japan and the Philippines — over disputed islands. Meanwhile, the U.S. Navy plans to send more ships to Asia, which China sees as an attempt to block its rise. America's allies in the region welcome more U.S. involvement, but they wonder about its staying power.

On a visit to Singapore this summer, Defense Secretary Leon Panetta announced that America's military was shifting its focus to the center of global economic growth: Asia.

"In a steady, deliberate and sustainable way," he said, "the United States military is rebalancing and bringing an enhanced capability development to this vital region."

Statements like that go down badly in Beijing.

One Chinese government spokesman said, "We hope that the American side respects the interests and concerns of the Chinese side and various parties in the Asia Pacific."

Panetta's pledge also raises a big question for American allies there: Can the U.S. follow through?

Huang Jing, who teaches political science at the National University of Singapore, asks: "Are Americans ready to increase investment in this area, or can America really afford that? Because, whatever strategy, you have to translate it into concrete policies, but so far, they haven't seen much of that."

For instance, the U.S. plans to deploy four coastal combat ships to Singapore. But analysts say they're too small to affect the balance of power.

Tim Huxley runs the Asia office of the International Institute for Strategic Studies, a leading think tank.

"I think there are many in the region who see a long-term pattern of American decline, who worry about the United States economy and what that will mean for defense spending and its ability to deploy forces in the long term," Huxley says.

The U.S. Navy has ensured security in the Asia Pacific for decades, allowing countries like Singapore — and later China — to build thriving economies. But America's financial problems and China's growing power are changing the equation.

"I think what's changed in the last few years is a battle for influence between the two major powers, which is much more obviously going on, to the extent that some people would talk about this in terms of being a sort of low-key, new Cold War," Huxley says.

Huang says countries are trying to strike a delicate balance. Some are building up their own navies, strengthening military ties with the U.S. and economic ones with China.

"Everyone is hedging because America is still dominant in security arrangements, so no one wants to go away from United States," Huang says. "They want to stay with the United States for security reasons. However, the entire economic dynamic is centered on China."

Many Chinese politicians think the U.S. is headed permanently downhill. But some Asian leaders caution China against overconfidence. Last month, Singapore's Prime Minister Lee Hsien Loong delivered this blunt message at the Central Party School in Beijing: "The U.S. will remain the dominant superpower for the foreseeable future. It is currently facing some very difficult problems, but it is not a nation in decline."

Zheng Yongnian, who directs the East Asian Institute at the National University of Singapore, says the prime minister was warning China not to underestimate the U.S.

"In international affairs, miscalculation or misperception sometimes leads to disaster — wrong decision," he says. "Not only Singapore, other powers will remind China to be realistic."

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