At least one of the 100-odd American ambassadors that President-elect George Bush must select could rank in importance with many of the Cabinet choices now drawing most of the nation's attention.

Bush must select the successor to former Senate Democratic leader Mike Mansfield, retiring after a record 11 years as ambassador to Tokyo.The job is important simply because Japan has become so important to America in the late 20th century.

Together the two countries account for 40 to 50 percent of world economic output. They have one of the world's most complex, emotionally charged and changing relationships.

Mansfield calls the U.S.-Japanese relationship the most important in the world and says that during his tenure in Tokyo it has changed from that of uncle-nephew to brother-brother.

Complicating the love-hate feelings often felt between the countries are deep cultural and language differences and Japan's new world importance.

In only four decades, Japan has transformed itself from a humble, defeated American enemy to a U.S. protege and loyal ally, an economic superpower and rival, U.S. creditor, landlord and occasional critic.

During the election campaign, Bush took positions on issues such as Japan's military and foreign aid role and trade.

To demands that Japan increase military spending and relieve some of the U.S. defense burden, Bush - a bomber pilot against Japan in World War II - noted that Japan's Asian neighbors still remember the war and "remain very sensitive to the issue of Japanese rearmament."

He suggested that Japan rapidly boost its share of global economic aid, a category in which it is about to surpass the United States. But that, too, could create other conflicts, because Japan is already becoming a rival to U.S. dominance of such international institutions as the World Bank.

On trade, Bush is expected to take President Reagan's general line of seeking to brake protectionist efforts to restrict Japanese imports into the United States while encouraging sharpened U.S. competitiveness.

Reagan and Yasuhiro Nakasone, the Japanese prime minister from 1982-87, developed a first-name relationship unprecedented in the two countries' history. Their personal connection helped the nations weather a rough period marked by U.S. pressure against Japanese domestic barriers, alleged unfair trade practices and insular thinking inappropriate for a country grown rich by exporting.

After 14 years as Senate Democratic leader, Mansfield was sent to Japan by Democratic President Jimmy Carter. In 1981 Reagan asked him to stay in the increasingly important post.