FROM WORLD WAR II until last year, New York was the world's leading center of international banking. But now Japan has most of the world's biggest banks, and Tokyo has overtaken New York in international lending. Similarly, London has surpassed New York in the volume of foreign exchange that it handles. These changes, minor in themselves, are further illustrations of the development of a world financial system with many centers of power of which none is dominant. That raises a question: Who's in charge?

Interdependence among national economies is nothing new. Most countries, including the United States, have been regularly and sharply affected by their neighbors' and trading partners' ups and downs since the middle of the 19th century. The periods of fast and stable growth have been those in which one country and one currency were the clear and acknowledged leader, taking the chief responsibility to manage and stabilize the whole system. Before World War I, that was Great Britain and the pound sterling. But after 1918 the British, who had the experience and the inclination to do the job, no longer had the necessary financial power. The United States, which suddenly had the power, had not yet acquired the experience or the inclination. The result was a very bad quarter of a century for the world's economy -- and not the economy alone.

After 1945 the United States ran the system with a careful eye to the mistakes made a generation earlier. From the late 1940s to the early 1970s, the world rode the great boom -- a prolonged surge of economic growth that has no equal in history. American dominance was finally eroded by the very success of American policy; it was designed to encourage growth worldwide, and it worked sufficiently well that in time the United States no longer overshadowed the other economic powers as it once had. The recent decline of the dollar and the corresponding rise of the yen and the mark have accelerated this redistribution of financial power.

Who's in charge now? A committee, more or less -- with the United States still at the head of the table but more of the votes shifted to the Japanese and the Europeans, notably the Germans. It works fairly well in technical operations. For example, it has presided competently over the long downward slide of the dollar's exchange rate. But most of the countries now sitting at the table are evading the rule that to keep the system going smoothly, the governments that run it occasionally have to sacrifice some of their own immediate interests and political purposes. The Japanese are moving very slowly to get their trade surplus down. The Germans feel no responsibility whatever to get their growth rate up. And the Americans, having thrown the world's finances badly out of balance by seven years of overspending, are trying desperately to squeak past one more election without making any unpopular changes.