President Obama and Chinese President Hu Jintao will meet in Washington, D.C., on Tuesday and Wednesday in a state visit meant to reset relations after a rocky year, but while dozens of major global issues will be on the table, one thing will be missing: trust.

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WASHINGTON — President Obama and Chinese President Hu Jintao will meet in Washington, D.C., on Tuesday and Wednesday in a state visit meant to reset relations after a rocky year, but while dozens of major global issues will be on the table, one thing will be missing: trust.

From the waters of the South China Sea to the halls of Congress to the coffers that hold Beijing’s deep foreign-currency reserves, the United States and China increasingly eye each other with suspicion.

Trade embrace

Locked in a multitrillion-dollar embrace of trade and debt, the leaders of the world’s two largest economies will work together where they can. But mutual suspicion and political realities mean that Obama and Hu are unlikely to announce major breakthroughs on sensitive issues such as currency reform or human rights.

“Overall, you’ve got a lack of trust, mutual trust,” said Drew Thompson, the director of China studies at the Nixon Center, a foreign-policy research center in D.C.

The Obama administration will use the White House meetings with Hu to prod China to let its currency, the yuan, float freely, making American exports more competitive; to help rein in North Korea’s nuclear ambitions; and to strengthen military-to-military ties, U.S. officials and private experts said.

American leverage is limited, however: China holds nearly $1 trillion in U.S. government debt.

Hu, whose term expires in 2012, apparently is hoping to burnish his legacy, improve China’s image in the United States — he also will travel to Chicago — and push for wider Chinese investment here. China lobbied for the official state visit, with all its pomp, for Hu. It’s the first for a Chinese leader since 1997.

The 14 months since Obama last visited China have been a roller coaster for Sino-American relations.

China suspended military exchanges last January to protest new U.S. arms sales to Taiwan, which Beijing considers a renegade province.

Then China began pressing maritime and territorial claims in East Asia, alarming the United States and its allies.

The administration pushed back. U.S. officials felt, until recently, that China had failed to dissuade North Korea from provocative actions, such as last year’s sinking of a South Korean corvette and shelling of South Korea’s Yeonpyeong island.

“Critical juncture”

Against that backdrop, Obama and Hu will attempt to set what’s arguably the world’s most important relationship on a smoother course.

“America and China have arrived at a critical juncture, a time when the choices we make, both big and small, will shape the trajectory of this relationship,” Secretary of State Hillary Rodham Clinton said Friday.

Clinton described the relationship as an increasingly complex global “entanglement” and said, “This is not a relationship that fits neatly into the black and white categories like ‘friend’ or ‘rival.’ “

In Obama’s first two years, she said, “We have seen some early successes and also some frustrations.”

The gripes don’t come only from the American side. Many Chinese accuse the U.S. of trying to stunt their country’s rise.

In the weeks leading up to the visit, diplomats from both countries have been negotiating a formal joint statement. But it remains to be seen whether Obama and Hu will issue a communique.

“There are some real limitations. And this will likely not be a sort of historic summit or transformational summit in U.S.-China relations,” said Michael Green, an aide to former President George W. Bush who’s now at the Center for Strategic and International Studies, a center-right research institute.

The misgivings are especially deep in the two countries’ military competition.

“I would be the first to admit that distrust lingers on both sides,” Clinton said. “The United States and the international community have watched China’s efforts to modernize and expand its military, and we have sought to clarify its intentions.”

Recent Chinese weapon developments, such as work on a missile designed to target aircraft carriers and the test of a stealth jet fighter during Defense Secretary Robert Gates’ recent visit to Beijing, may not be as alarming as headlines suggest. Both systems appear to be years from deployment, and are of unknown quality.

Yet to some, they suggest that China is looking not only to reinforce its dominance in the long-standing dispute about Taiwan but also to counterbalance the U.S. presence in the East China and South China seas.

Many observers suspect that these developments are motivated partially by worries from China’s leadership — particularly in the military — that the U.S. is trying to hem in China’s rise by strengthening ties with neighbors such as Japan and South Korea, and by emphasizing U.S. naval superiority.

“To be honest, I think for the moment such (weapons) developments are very much on paper,” said Zhu Feng, the deputy director of the Center for International and Strategic Studies at Peking University. “What actually worries me most is some kind of spiraling tensions between both sides.”

Finally, the two countries have irreconcilable differences over freedom of expression. When Obama and Hu make toasts at their state dinner, 2010 Nobel Peace Prize winner Liu Xiaobo will remain in a Chinese prison.

Tom Lasseter in Beijing and

Kevin G. Hall in D.C.

contributed to this report.