(FORTUNE Magazine) – Judging from the confident forecasts by a chorus of experts, the Pacific Century should be dawning about now. Nearly 30 years ago, futurist Herman Kahn argued that by the year 2000, Japan was sure to become the world's No. 1 nation. His influential book The Emerging Japanese Superstate depicted the triumph of a new brand of capitalism, under which wise government bureaucrats set the course while diligent workers who respected authority labored to create national wealth. More recently, trend forecaster John Naisbitt roamed the lecture circuit trumpeting that "Asia will become the dominant region of the world--economically, politically, and culturally." Many Asian leaders, of course, echoed that idea.

Well, it hasn't happened. Economic stagnation for most of the past decade has made Japan--still Asia's biggest economy by far --look more like a supermess lately. And the Asian financial crisis in mid-1997 has hampered the rest of East Asia.

And yet the predictions keep coming, this time about China. Says Fred Hu in a new Goldman Sachs report: "It is likely that within the first two to three decades of the next millennium, China will overtake the U.S. as the largest economy." He also predicts that by then Chinese consumers will have a purchasing power "larger than all of Europe's."

Even if China does grow that large, it is unlikely to dominate the world economy in the next century. And the same holds true for the rest of East Asia too. Why? Fundamentally, the old Asian success formula has failed miserably as a model for Asia as well as for the rest of us. The government bureaucrats and autocrats who claimed to have all the answers for spurring economic growth stumbled over their own inherent weaknesses--rampant corruption, collusion with favored companies, and cronyism that funneled questionable loans to friends and family of government leaders. Says Kishore Mahbubani, Singapore's cerebral ambassador to the United Nations: "The key lesson that all East Asian economic managers have learned [from the financial crisis] is that they are accountable not only to domestic actors but to the international financial markets and their key players."

That doesn't mean, though, that we should count Asia out. Over the next century it will continue to play a huge and crucial role. The region's remarkable progress over the past three decades is genuine. Never before in history have nations climbed from poverty to prosperity in one generation--as South Korea did--an accomplishment that indeed seemed like a miracle. The Asian financial crisis, a mere blip in the span of a century, has forced the region to start reforming its worst weaknesses--from shaky banking systems to corrupt business practices. Most crisis-afflicted economies, such as Thailand and Korea, are already growing again. Moreover, the fundamental strengths that originally ignited much excitement about Asia's prospects are alive and well. They include high savings rates, robust investment in education, relatively young populations, and ambitious entrepreneurs.

Over much of the next century East Asian economies almost certainly will continue expanding faster than mature Western economies. The region will serve as both a major production base and a voracious market. Asia today is the world's dominant producer (and a significant consumer) of steel, ships, semiconductors, and notebook computers. Judging from the speed at which Asia is plugging into the digital world, it will stay at the forefront in applying new technologies for communications and electronic commerce. Taiwan, for instance, is a supplier and designer of sophisticated components for computers and mobile phones. Hong Kong and Singapore are hurrying to become hubs for cyber-commerce.

So Asia may someday be able to lay claim to a Pacific Century. Trouble is, to get there it must first change some of its vaunted "Asian values." These include a respect for authority and a willingness to sacrifice individualism for the good of the society. It turns out, however, that these supposedly special values--which some government leaders still claim to be potent economic drivers--are glaring weaknesses. In fact, they get in the way of economic development.

It is true that Asian values served the region well for years. Says Ungsuh Kenneth Park, a thoughtful Korean economist: "East Asian societies achieved rapid growth with strong governments, meek people, and wide cooperation for achieving national goals. This is the sine qua non for every society, anywhere in the history of mankind, at an early stage of economic and social mobilization." But the world is changing, and Asia must change with it. Park continues, "Once basic needs are met, people everywhere demand greater participation in the decisions that shape their lives."

The "Asian values" argument has often served as a convenient justification for authoritarian regimes. "It is altogether shameful to cite Asian values as an excuse for autocratic practices and denial of basic rights and civil liberties," Malaysia's former Deputy Premier Anwar Ibrahim, a reform-minded Muslim intellectual, has said repeatedly. He should know, having been removed from office last year, jailed, beaten by the police, and convicted of dubious corruption charges. His real crime apparently was challenging Malaysia's Prime Minister Mahathir Mohamad, who claims that Asian values are superior to the "moral degeneration" of the West. Mahathir is on the wrong side of history, though.

In the next century Asia will travel slowly and fitfully down the long road toward democracy and the rule of law. Its educated and ever-increasing middle class will no longer bow to the will of strong-man regimes. This assertive spirit is clearly visible in Thailand, Taiwan, Indonesia, and South Korea, which over the past decade have replaced dictatorial regimes with various forms of representative government. The sharp pains caused by the Asian economic crisis last year, for example, prompted Indonesians to dump President Suharto, who made all the big decisions for three decades and enriched his friends and family but allowed no audible dissent. Indonesians are struggling to build a more open society, in which officials are accountable to the public.

Even China, where the Communist Party has maintained a monopoly on power for 50 years, will need to rely on the consent of the governed in the 21st century. Chinese leaders argue that stability is what counts. But a society going through the traumatic changes of rapid development, which produce many losers as well as winners among its citizens, especially needs honest administration and an independent legal system. Without the rule of law, foreign investors as well as Chinese citizens are subject to the shifting whims of officials. Lee Kuan Yew, who built modern Singapore and is no champion of Western-style democracy, foresees China's going "from a centralized to a more participatory system of governance" within the next 50 years. Lee also warns that China must clean up its "most pernicious problem," corruption embedded in its administrative culture, or face a dangerous political powder keg.

Japan will suffer for decades to come from a tribal reluctance to disturb its own social harmony by freely allowing failing corporations to restructure. Americans and Europeans, who once eagerly studied Japanese management techniques in the '80s, have belatedly discovered the dark side of the system. Even the most troubled Japanese companies are pressured to continue employing surplus workers and retaining inefficient suppliers, while collusion between government and business often hides the true financial state of banks and corporations. Allowing bureaucrats to set industrial priorities has left Japan surprisingly uncompetitive in such growth fields as financial services and computer software.

A new challenge for the Japanese lies just ahead. By the year 2025, Japan will become the world's leading geriatric nation, with nearly 26% of its people age 65 or older. Karel Van Wolferen, a Japan expert who once viewed the country as almost omnipotent, now hopes that Japan somehow will succeed in "reinventing" itself. Perhaps as a retirement community?

So the new century, it seems, will belong not to Asia, America, or any other single geographic entity but to an increasingly interdependent world economy. Welcome to the Global Century, in which innovative Asians will flourish, but not dominate.