The summits of allied leaders in London and Houston over the last two weeks demonstrated anew how the end of the Cold War is changing the chemistry of power among nations, shifting from an atmosphere of stark East-West confrontation to a multipolar world in which the United States is but one of several leading players.

According to diplomats, experts and administration policy-makers, President Bush chose to exercise U.S. influence selectively rather than trying to impose it across the board at both the North Atlantic Treaty Organization meeting in London and the Houston summit of leaders of the major industrial democracies.

He pushed hard for progress on reducing agricultural trade subsidies in Houston, and he sought to refine alliance military doctrine and strategy in London. But he readily deferred to the rising political strength of two economic powerhouses, West Germany and Japan, when they demonstrated their determination to pursue their own interests in financial aid and loans to the Soviet Union and China.

"It doesn't work . . . that you have to march in lockstep on all these questions," Bush said. "We're dealing in entirely different times. Earlier on, in terms of the alliance, we had a much more formidable military opposition. Now we see the Warsaw Pact in almost a state of disarray, we see troops coming out, we see democracies replacing totalitarian systems. So you have an entirely different era."

This outlook marks a shift from the U.S. approach during much of the 1980s. President Ronald Reagan came into office determined to reassert U.S. dominance in the world as a counter to the Soviet threat. He pushed his alliance partners to follow his direction. For example, in 1981-82, Reagan tried to impose sanctions on Western European firms that were helping Moscow construct a natural gas pipeline. Reagan's call for sanctions touched off a furor among the allies.

But the receding Soviet threat and shifts in the global economy have made such episodes seem a relic of an earlier day. Bush has encouraged the trend back toward a multipolar world in which the United States shares economic and political power with its partners.

Taking note of the shifting arrangements, British Prime Minister Margaret Thatcher observed in Houston, "There are three great groups of nations at the summit, one based on the dollar, one based on the yen, and one based on the deutschmark."

"I hope America does not have the idea they are sort of out of it," French President Francois Mitterrand said. "That is not the case. The threat from the Soviet world has been reduced. Because of that, Europe can assert its personality."

The most assertive nations among the Western democracies have been West Germany and Japan. Seeking to ease Soviet concerns about German unification, Chancellor Helmut Kohl has moved quickly to supply credits and loan guarantees to Moscow and urged the West to join him. Japanese Prime Minister Toshiki Kaifu came to Houston determined to resume a $5.8 billion loan program to China that had been suspended after the Tiananmen Square crackdown on pro-democracy demonstrators. Both received a green light from Bush to go their own way even though the United States did not want to follow.

Even if Bush wanted to go along with the German and Japanese initiatives, he simply cannot afford to do so. Strained by a large and continuing budget deficit, the United States cannot shoulder expensive new international obligations, and is moving toward retrenchment of its overseas military establishment. Ironically, the United States, which began the 1980s seeking to reassert its global influence, now finds itself strapped for resources just as its goals of spreading democracy are being fulfilled.

"It's as much economic as it is political force," said Timothy W. Stanley, president of the International Economic Studies Institute. "We're consciously trying to guide this new world in ways that are in our interests -- and that means give people their head. You can't say to the Japanese, we want your help to carry the burdens, but you can't give any money to China." Likewise, he said, "Germany has a healthy interest in buying reunification and they are willing to put up the money to do it. That gives them an edge in future market share if the Soviet economy ever gets healthy."

"I don't see it as a negative," he said. "It is a positive acceptance of the fact that in today's world we need the active participation, help and collaboration of other countries."

Zbigniew Brzezinski, former president Jimmy Carter's national security adviser, cautioned that the shift toward a multipolar relationship among the allies is not wholly new, and bears similarities to a period of the 1970s under Carter and former president Gerald R. Ford.

"The really significant differences," he said, are that "Japan has ceased to be just an economic superpower, but is in the process, cautiously, of being a political superpower. And secondly, the political lead has passed from France to Germany, and Britain to Germany."

The collapse of Cold War tensions has also been a major reason for the shifts. "The East has disintegrated and hence American leverage that derives from deterrence is much less salient," Brzezinski said. Other factors such as technological prowess and economic power "are becoming more significant," he added. "But even in those, I don't think one should underestimate U.S. capacities. I am a little wary of new historical eras in which American leadership is finished."

Bush often has said he disagrees with those who have predicted that American global influence is in decline, but at the same time he has not tried to throw that influence around at all costs. "There's a certain greater multipolarity that we're trying to shape," said a senior U.S. policy-maker. "We have to get out in front of it." This official cited the letter that Bush sent the allied leaders before the NATO summit, which provided the framework for the final communique, and Bush's strong drive in Houston for progress in eliminating agricultural trade subsidies.

At the same time, there are many uncertainties about what kind of policies will result from the more diffused post-Cold War arrangements, including what direction will be taken by a unified Germany, by Japan, and -- most uncertain of all -- by the Soviet Union. Many analysts think that as long as Moscow remains focused inward on its economic crisis, there will be less support for regional conflicts around the globe, another positive byproduct of this period.

Leonard S. Spector of the Carnegie Endowment for International Peace said "one element of the multipolarity is the growth of very powerful regional states," and some, such as Iraq, may pose new challenges to American interests. But in other areas, he said, "the Soviets are pulling back. Regional powers that have been adversarial to the U.S. might not be as dangerous because they don't have that backing of the Soviet sponsor, as they did. In the multipolar world, the American pole is still going to have a lot of reach and influence, where the Soviets are going to have less."