As the tumult and the shouting dies and the captains and kings prepare to part, Americans are beginning to assess their place in the postwar world. There is a brief moment of rejoicing before the bills come due.

For a start, politicians and pundits assert thankfully that the "Vietnam syndrome" is at last dissipated. By this they mean that the lack of self-confidence, lack of faith in the armed forces and remaining divisions between supporters and opponents of the Vietnam War have all been healed.Certainly the armed forces have come through the gulf war with great credit. This was the first clear victory in a major war since 1945, and though in fact Iraq was not much of an enemy, the American air force and ground troops behaved with striking professional competence and flair. They will come back to a heroes' welcome, which was not the case after Vietnam.

That is all to the good, and people are enjoying a brief moment of domestic unity. It may not last very long: Republicans are already trying to paint the Democrats as unpatriotic, because most of the party in Congress voted against the war, and the Democrats are doing their best to remind people that there's more to government than beating up incompetent Third World dictatorships.

The serious questions that are now being asked are: What should the United States do with its victory, in the Middle East and elsewhere; and has that victory done anything to solve the country's other problems?

Americans were delighted with their "smart" weapons - those bombs that dropped down chimneys and those missiles that hit Iraqi tanks every time. For years people have deplored the failures of American technology, in matters large and small.

The most conspicuous failure was the Challenger disaster, the space shuttle which blew up in 1986, killing seven astronauts. NASA has never recovered: The latest shuttle flight has just been canceled because cracks were found in it. A country that put men on the moon is incapable of keeping its main space vehicle working.

On a smaller scale, the United States has not only lost its domestic television, camera, personal computer and electronics industries to Japan, it is now losing its ability to make microchips and is rapidly falling behind in the next generation of computer technology.

As Americans drove to work in Japanese cars, listening to Japanese-made radios, using Japanese (or Korean)-made computers, they used to grumble that their country could never get anything right. The star performance of F-15s, F-18s, smart bombs and Tomahawk cruise missiles has restored self-confidence in national technology.

This sense of achievement will not last long. Victory in the gulf war has done nothing to reduce the trade gap or the budget deficit. In all the self-congratulatory analyses of who has done well out of the war (commentators start with George Bush and move on down the American line) none mentioned the great victor, Japan.

The Japanese can now be assured that their oil imports will cost less than $20 a barrel for the rest of the century, and that their trade surplus - and therefore their ability to buy up American companies - will continue to rise.

Germany has done well, too, for the same reason - and by extension, so has Eastern Europe. The nightmare hanging over them all was that Saddam Hussein would win and double the price of oil. That, of course, was his chief objective - and if he had succeeded in annexing Kuwait, he would have achieved it. Saudi Arabia and the emirates would never have dared oppose him.

Oil at $40 or more a barrel would have ruined Poland, Hungary and the rest, not to mention Africa, Asia and South America, and driven the United States into deep recession, as in the 1970s. All these places owe America a great deal.

The United States is already wondering if it can cash in on this gratitude, and reluctantly, knowing the history of such sentiments, concludes that it cannot. It may be the only superpower left in the world, but that could turn into a very expensive privilege.