President Barack Obama began a nine-day trip to East Asia yesterday, with stops in Japan, Singapore, China and South Korea. Given the United States' important relationships with these countries, his first visit to the region as president is important.

Mr. Obama gave a major speech on Muslims and the Middle East in Cairo in June and an Africa policy speech in Ghana in July. The message he plans to deliver in Tokyo will presumably call the tune for what his administration hopes to achieve in East Asia.

In Japan the Obamas will meet the emperor and empress. Talks with newly elected Prime Minister Yukio Hatoyama will deal with economic and military matters. Japan remains the world's second-largest economy and coordination with it on efforts to exit the world recession is essential.

The new Democratic Party in control of Japan's government seems set on changing the military relationship with the United States, including the status of U.S. troops stationed there. In spite of his interest in nuclear disarmament and his Nobel Peace Prize, Mr. Obama apparently does not intend to visit Hiroshima or Nagasaki.

While in Singapore, Mr. Obama will become the first U.S. president to attend a summit of the Association of Southeast Asian Nations. That 10-nation body includes Myanmar, with which the administration launched talks earlier in the month. He also plans to meet with Russian President Dmitry Medvedev there.

Mr. Obama will spend four days in China, the centerpiece of the trip. Probably the most important item on his agenda there will be synchronization of the huge American-Chinese trade and financial relationship for the best interests of both countries. Recovery from the recession for the Chinese means increased exports to the United States, widening an already unfavorable (from the U.S. point of view) balance of trade.

Given America's soaring national debt, it also will be necessary for the Chinese to continue to loan the United States money to keep the place afloat and finance its wars. Mr. Obama will have to mention the issues of Taiwan and Tibet, although he will not want to agitate his Chinese hosts unduly. A "town hall" meeting he has scheduled for Shanghai could be the most sensitive moment on the entire itinerary.

The South Koreans would like to see action on a free-trade agreement completed, but free trade is considered toxic by some of Mr. Obama's U.S. supporters. Relations with North Korea will also loom large, underlined by a recent nasty naval skirmish.

There will be lots to do. Mr. Obama will probably be glad to get home at the end, and will find America's health-care wrangles comforting compared to some of the issues he will face in Asia.

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