Even as the United States and Soviet Union struggle to disentangle themselves from the regional conflicts of the Cold War, the superpowers were presented last week with a stark picture of the new hostilities they may confront in an era of East-West cooperation.

From Afghanistan to Cambodia to Angola and Nicaragua, the United States and Soviet Union are trying to shut down the Third World conflicts they fueled in the 1980s. But in Iraq's sudden invasion of Kuwait, the United States and Soviet Union are facing a conflict that began well beyond their control, according to administration officials and private analysts.

The irony of the post-Cold War period may be that while Washington and Moscow cooperate more frequently around the globe, even together they cannot ensure worldwide stability and tranquility. While the nuclear superpowers still wield enormous clout, there is growing evidence the East-West military competition is being supplanted by a surge in global competition for economic resources.

Those nations with economic surpluses, such as prospering Japan and West Germany, are reasserting themselves in the West. In the Third World, Iraqi President Saddam Hussein invaded Kuwait in a grab for oil and money. And the Soviet Union, falling into economic collapse, is turning inward from its once-expansionist aims. Many Soviet clients, such as Vietnam and Cuba, are finding their resources drained and Moscow's subsidies drying up.

The consequences of these pressures have been amply illustrated in the series of recent meetings between Secretary of State James A. Baker III and Soviet Foreign Minister Eduard Shevardnadze. First in Paris last month, and again in the Soviet Union last week, they talked about resolving the conflicts in Cambodia and Afghanistan that have sapped money and political capital from both nations for a decade.

In an unprecedented display of cooperation unthinkable only a year ago, they condemned the "brutal and illegal invasion" of Kuwait, and the Soviets, the largest arms suppliers to Iraq, suspended arms deliveries to Saddam.

The decision to do this marked what Shevardnadze acknowledged was "a rather difficult" turning point for Moscow. According to U.S. officials, Baker and Shevardnadze also talked privately in their Moscow meeting about how to persuade other nations to join in isolating Iraq, a long-standing Soviet ally.

The two ministers also discussed possible military responses, and Shevardnadze made it clear to Baker that the Soviets "did not want to see a quick resort to military force," a senior official said.

This official added that the talks could help set a pattern for further cooperation on regional conflicts in the years ahead. "Something broader is going on in the changing pattern of U.S.-Soviet relations," the official said, as both nations position themselves to focus on the "threats of the '90s," such as Saddam.

According to U.S. officials, the U.S.-Soviet cooperation has been evident in more routine ways, as well. When two rebel groups began closing in on President Samuel Doe of Liberia recently after a bloody seven-month offensive, Moscow discovered that a group of Soviet diplomats had been cut off in Monrovia and could not be reached. The Soviets turned to the United States for help, and American officials helped reestablish contact with the stranded delegation.

But many government officials and private analysts acknowledge that there are limits to how far Washington and Moscow can go in changing the behavior of others. "The world's trouble spots don't seem to be Soviet and American," said Michael Mandelbaum of the Council on Foreign Relations.

At the Washington summit, for example, President Bush and Soviet President Mikhail Gorbachev announced a joint effort to rush food relief to starving Ethiopians trapped in a civil war.

Despite the military might of both nations, however, the planned air and sea lifts of food have been frustrated by refusal of rebels fighting the government to allow planes and ships to arrive.

The United States and Soviet Union have vital interests in the Persian Gulf. But in the first days after the invasion, neither seemed in position to change the behavior of Saddam.

Short of an attack on Saudi Arabia by Iraq, the two superpowers and their allies are instead trying to squeeze the Iraqi president by shutting down his oil flow -- an economic response that may take some time to have an impact.

"Making a statement in Moscow is good to start, but what do you do tomorrow?" said Judith Kipper, a Middle East analyst at the Brookings Institution. "The United States and the Soviet Union are in the same little boat in this tumultuous sea. Neither of us has very much influence. The possibility of influencing the situation is extremely limited after the fact" of the invasion.

A danger in the new post-Cold War climate is that the absence of Washington and Moscow as active players may contribute to a power vacuum like the one that Saddam suddenly has tried to fill in the Persian Gulf, Kipper said.

"The smaller powers, the regional powers like Iraq no longer have to look over their shoulder" at the United States and Soviet Union, she added. "They can no longer turn to Washington or Moscow with the blackmail politics that 'you have to help us.' They can act with impunity to arrange their own little problems -- regional powers that are non-democratic, that are desperate, that have their own view of how things should work in their area."

Nonetheless, the regional conflicts that flared in the last decade with support from the Soviet Union and the United States are winding down, with both superpowers trying to disengage.

For the United States, these conflicts were viewed as a way to respond to Soviet expansion in the Third World during the 1970s and 1980s without directly committing U.S. forces -- a policy called the "Reagan Doctrine" by conservative activists. But according to officials, both superpowers were reaching the exhaustion point when Bush took office.

For the Soviets, it was economic exhaustion, while for the Americans it was primarily political, as constant White House-Congress battles over places like Nicaragua took their toll.

But while the Nicaraguan war ended with an election in which the Soviet-backed Sandinista regime was dumped by the voters, officials said it is likely that the conflicts in Afghanistan, Cambodia and Angola will end less neatly. "All the rest are going to be us pushing back and saying, 'You guys figure it out,' " a senior policy-maker said. "In neither Afghanistan, Cambodia or Angola are we going to be able to engineer an outcome. It is much less clear."