THE AMERICANS' and the Saudi Arabians' views of each other these days tend to be clouded by a sense of grievance. The United States has provided the Saudis with military security all these years, and bought their oil at such large and rising cost; why have they now turned querulous and unhelpful? The United States has given Saudi Arabia very effective protection against one kind of threat - conventional attack by a modern army like, for example, the Soviet Union's. But the Saudis, looking around them, see many othe threats, of which some are much closer than the Soviets. They note that the United States was able to do little for its friends and clients in Somalia and Iran. American military power is not very useful against the guerrillas, civil revloutionaries and saboteurs that have been at work among the saudis' neighbors.

In its efforts to reassure the Saudis, the United States has done precisely the opposite. When it sent a special mission of U.S Air Force F15 jets to Saudi Arabia, it mainly demonstrated the difficulties that it would encounter in any serious military operation in that region. The United States sent two AWACS planes, stuffed with radar equipment, as symbols of its advanced military technology. But the AWACS is not much help in dealing with guerrillas.

The Palestine Liberation Organization hinted last fall that it might move on Saudi oil installations. The Saudis do not take the threat very seriously at the moment, but it is not the kind of thing that any Middle Eastern government wholly ignores. Oil wells, pipelines and storage tanks are inherently fragile and hard to protect. It is a matter of some perplexity to the Saudis that Americans, with huge stake in the flow of oil, do not seem to focus on the the unpleasant possibilities there.

The United States has been pressing Saudi Arabia to support the peace between Egypt and Israel. It has also been pressing Saudi Arabia to produce more oil, restrain the rising price and support the dollar. Each of those policies is very likely to bring the Saudi government into conflict with the radical Arab governments and political movements tha are hostile to the peace, hungry for much higher oil prices and indifferent to the future of the dollar. The Saudis seem to feel that the United States is asking too much of them, and that they cannot bear the load. The United States keeps telling the Saudis that their cooperation is essential to world stability. The relationship is an exercise in mutual dismay. Each side is having to learn to lower its expectations of what the other may provide.