Chinese Vice President Xi Jinping has completed his second visit to the United States. Mr. Xi’s trip reciprocated last year’s visit to China by U.S. Vice President Joe Biden. That trip launched a “get acquainted” effort with Mr. Xi, the man set to become China’s president next year.

Mr. Xi had his own agenda. He was trying to establish his credentials as a leader. Throughout his visit, he was speaking to two audiences: his hosts and the Chinese back home. To the former, he was attempting to build a relationship that would anchor the two countries’ relations when he takes office.

At the same time, he was showing the Chinese people that he could represent their country and defend its national interests.

Mr. Xi first visited the U.S. in 1985 as part of a provincial tour to learn about U.S. agriculture. That trip took him to Muscatine, Iowa, a farming community in the American heartland. Muscatine is the symbolic centerpiece of last week’s visit, providing a “homey” contrast to the starched formalism of the Washington stop.

Mr. Xi’s handlers were hoping for a “cowboy hat moment,” like that which occurred during Deng Xiaoping’s 1979 visit to Texas, when he donned a cowboy hat , a gesture that is generally credited with transforming U.S. perceptions of Deng and his country.

Mr. Xi’s task is tougher. Then, Deng could use the Soviet Union (or the lingering resentments of Vietnam) as the implicit reason for the two countries to cooperate.

Today, the U.S.-China relationship is rife with tensions; it’s as much a competition as it is a partnership. The two countries go head to head on most policy issues, from international diplomacy to economic and military relations. Yet Mr. Xi, along with his U.S. counterparts, must signal the intent to work together while defending national prerogatives.

In Washington, Mr. Xi received the red carpet treatment. He was treated to a state dinner at the White House, a one-on-one session with President Barack Obama (which ran overtime), had intense conversations with administrative officials and congressional leaders, and had a highly publicized meeting with U.S. Secretary of Defense Leon Panetta.

The last meeting may prove to be the most significant, since military-to-military interaction between the two countries has been the most inconsistent — and hence worrying — of all the bilateral discussions.

Mr. Xi spoke not only of the need for enhanced military discussions but of a desire to improve those talks.

In their meeting, Mr. Biden outlined a long list of U.S. grievances: trade practices, intellectual property protections, human rights policies and diplomatic differences — most recently over Beijing’s veto of a United Nations Security Council resolution to try to halt the violence in Syria. Mr. Xi countered that the U.S. needed to check its protectionist instincts, put its words into deeds and do more to safeguard peace and stability in East Asia.

Most significantly, Mr. Xi called on the U.S. to treat China with respect and acknowledge his country’s core interests.

While welcoming the U.S. “pivot” to Asia, he warned the U.S. to “truly respect the interests and concerns of countries in the region, including China.”

There is little indication that either side had much impact on the other’s thinking. In fact, this visit was not intended to change the trajectory of the bilateral relationship.

Indeed, no one believes that Mr. Xi was selected to the highest level of the Chinese leadership to change his country’s policies. Rather, his most pressing assignment is managing China’s relationship with the U.S. as his country attempts to deal with the stresses and frictions created by its breakneck modernization.

Mr. Xi will not be expected to handle this on his own, but he will be the face of Chinese diplomacy as it tries to deal with both internal pressure and an evolving external environment.

In this effort, the U.S. will play a critical role. Ideally, it will be a partner for China, working with it to tackle critical challenges. That is the preferred course of American politicians, who understand that China is too large to be ignored and capable of blocking Washington’s plans in almost any arena.

In the worst-case scenario, the U.S. could become an adversary of China, effectively thwarting its ambitions for a leading regional and global role.

Mr. Xi must keep the bilateral relationship moving forward. To do so, he will accentuate the positive while securing China’s national interests. It can be a delicate balancing act, especially when those interests appear to clash with those of its neighbors. As Mr. Xi tries to build a cooperative relationship with the U.S., he must do so with an eye firmly fixed on political dynamics at home.

Political transitions in authoritarian states are invariably fraught, as factions fight it out behind the scenes to secure posts, prestige and the associated spoils. The stakes are only going to increase as the tensions within China increase.

Even as heir apparent, Mr. Xi has his work cut out for him. A forward-looking relationship with the U.S. should help him , but he must be ever vigilant about the price he pays.

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