AMERICAN TROOPS are not in the Saudi desert to defend $1-a-gallon gasoline. Neither are they there to defend democracy, for that term applies to none of the Persian Gulf states. But the United States and its allies in the desert have clear and compelling reasons to be there.

An oil crisis alone -- a soaring price and the threat of shortages -- would be unlikely to push the United States to the point of war. The price of oil is somewhere around $27 a barrel. In early 1981 it went over $35 -- in today's dollars, that's well over $50 a barrel -- and there was no impulse to send aircraft carriers to the Gulf. But oil is certainly part of the calculation that makes Iraq's invasion of Kuwait dangerous to the rest of the world.

Iraq's aggression is the central fact that has created the alliance of Arab, European and U.S. forces that now surrounds the aggressor. There have been other cases of aggression in recent memory that the world has let pass with a less decisive response. But the circumstances in Iraq's case would make complaisance there intolerably costly.

Suppose that the United States and the others had not sent troops and ships or shut off Iraq's trade. Saudi Arabia, finding itself isolated and wholly vulnerable to attack, would -- under the best of circumstances -- have had little choice but to accommodate Iraqi demands for higher prices. These might not necessarily have been high enough to produce a catastrophe in the industrial world; if they weren't, but were, say, as high as prices were six or seven years ago, Iraq's oil revenues would have tripled. What do you suppose it would have used that money for? Clinics? Schools?

The present Iraqi regime has for years funneled vast resources of oil wealth -- its own and subsidies from its neighbors -- into armaments and its military ambitions. With a huge increase in those revenues, won by armed conquest, it would move into an entirely different category of power. Iraq, according to careful estimates here, could develop nuclear weapons in perhaps five years. It already possesses medium-range missiles, and the technology to extend their reach is for sale. By its use of poison gas, Iraq has already demonstrated that it feels no need to observe its treaties.

Secretary of State James A. Baker, testifying before Congress, emphasized a hope that the present crisis will launch a new international effort to bring under control the proliferation of nuclear, biological and chemical weapons, including missiles, in the Middle East and worldwide. He spoke forcefully of the need for a new security structure for the Persian Gulf. Clearly the presence of American forces is going to be a necessary element in that security structure for a long time.

The Saudi desert is not a pleasant place to spend time, but the troops gathering there are doing a crucially valuable job. If you doubt it, consider what would be happening in their absence.