BEIJING -- In the heady, waning days of Beijing’s Olympics, young Chinese took to greeting each other gleefully: “How many gold medals have we won today?”

The evident pride of many Chinese in the Olympics offers a glimpse of things to come after the games end Sunday. As the foreign teams desert Beijing, China will revel in deserved accolades for an impressively run Olympics and admiration for the prowess of its athletes, who dominated the gold-medal tally.

But for Chinese and their government, the Olympics was not just about China’s rank on the medals table, but also about its international standing. “For its future, China needs to become more international, and the Olympics was an important step in that,” said Luo Qing, a specialist on China’s image at Communications University of China. “So it was crucial that the international community pay us due recognition.”

Whether China received the respect it hoped for is an issue vital for the world as it learns to accommodate the ambitions of the rising, powerful China so fully on display in Beijing. Success in the games could produce a China more comfortable with its place in the world. A confident government may be more willing to work with the U.S. and other powers on global hotspots. At home, it may take bolder steps to address rising demands for greater social justice to close a widening gap between the newly well-off and working-class Chinese.

At the same time, a China that feels triumphal and under-appreciated could touch off a prickly nationalism. The communist government would turn more repressive at home and more assertive abroad, bucking efforts to address climate change and nuclear proliferation.

Already there are signs that an emboldened government is readying a clampdown on often violent separatism in its Muslim west and purging Tibetan monasteries of pro-independence clerics.  Meanwhile, with some Internet sites unblocked for the Olympics, some Chinese in Beijing have thrilled to accessing Amnesty International and Western media sites but are now preparing to lose that newfound freedom.

“The Olympics are a prism for the conflicts, emotions and tendencies that are being worked out—and worked out in public,” said Zha Jianying, a China-born, U.S.-based author writing a book about the Olympics and China.

Having come from poverty to relative prosperity in a generation, many Chinese have looked to the Olympics as a celebration of their achievements and of China’s return to its historical greatness. The Chinese government and many of its people “hoped to show the world a China that, after 30 years of rapid development, has not been seen in hundreds of years,” the Global Times newspaper said in a commentary.

The dual needs to do well for the home audience and to be seen as worthy hosts by the global community formed the subtext of the 17-day Olympics, played out at sporting events, in media coverage and on the streets.

Audiences and state media veered between outbursts of patriotism and flashes of internationalism, egged on by a government that ordered up good sportsmanship. When the Chinese women’s table tennis team won, on a day halfway through the games when China grabbed eight gold medals, newspapers pasted their pictures on Page One and hailed the runaway lead in medals.

Yet they also roared for Michael Phelps in his quest to win eight golds and Kobe Bryant and the rest of the U.S. basketball team. Ni Weiping, a grand master of the chess-like strategy game Go, used his blog to savage the Chinese coach of the U.S. women’s volleyball squad, Lang Ping, as a traitor after it edged out the heavily favored Chinese team; in response, Internet postings criticized Ni for being narrow-minded. “Cheering for foreign teams would have been unimaginable four years ago, much less 20 years ago,” the Titan Sports Weekly said.

Beyond the measured good will, Beijing displayed a technical proficiency in putting on the games. Buses ran on time, the city gleamed invitingly with banners and flowers and everywhere athletes, foreign journalists and tourists turned there were legions of helpful, youthful volunteers.

Many of the same qualities that made the games successful also aggravate concerns about the kind of world power China wants to be.  The eye-catching venues, those unfailingly smiling volunteers and the cast-of-thousands opening ceremony—which Beijing said it kept rain-free by firing silver iodide capsules into the sky— underscores the government’s authoritarian powers and its ability to spend $40 billion on an Olympics with barely any public dissent.

“This is the beauty of dictatorship: They can do many things that other countries cannot do,” said Guoqi Xu, a historian and author of the book “Olympic Dreams: China and Sports, 1895-2008.” “You have to remember they even controlled the weather. No other country would do this.”

China also rewrote some commitments made seven years ago when it was awarded the games. After promising that the Olympics would improve human rights and that foreign media would have unrestricted access, the government arrested civil rights campaigners and kept many Internet sites blocked. It designated three parks for public protests but then refused to let anyone use them.

Criticisms in word or deed sometimes set Chinese bristling, confounding hopes that the Olympics would serve as a bridge to greater understanding of China. When foreign supporters of Tibet’s independence from Chinese rule breached the prohibition and staged a small protest on Tiananmen Square, they were surrounded by young Chinese men—some wearing red-and-yellow headbands—who shouted “Get out! Get out!”

“The Olympic Games are all about sport. It is about the Olympic spirit. It is not a political platform,” Beijing Olympic organizers spokesman Wang Wei said this past week in his frequently testy exchange with foreign media.

Away from the sports, the disputes highlighted glaring breaches between China and the rest of the world that Chinese hoped the Olympics would close.

“This one single event is not enough” to close the gaps, said Victor Yuan, chairman of Horizon Group, a research and polling company in Beijing. Yuan said the government, however, is convinced that the games began changing foreign minds about China. It has two other international events in planning for 2010, the World Expo in Shanghai and the Asian Games in Guangzhou, to further reshape impressions.

“People now realize it’s not such a simple matter. It’s not just like opening the door and inviting guests in,” said Luo, the image expert. “China’s road to the future will be long.”