Any list of America's postwar military client states would include embattled countries such as Israel and South Korea, for a time South Vietnam and Cambodia, or today, El Salvador.

Yet the nation that actually relies more than any on a U.S. military presence for its security is rarely spoken of as an American dependent. It is Iceland, and maintaining a low profile for that U.S. role is crucial to preserving a relationship that is vital to both nations.

Strategically located at the crossroads of North Atlantic shipping lanes in an increasingly busy arena for Soviet air and naval activity, Iceland is the only member of the North Atlantic Treaty Organization with no armed forces of its own. The government's sole weapons belong to a six-vessel Coast Guard intended to shoo away fishing poachers.

Iceland's entire defense, therefore--and for that matter a substantial part of its fishing-based economy--is supported by the United States and has been almost continuously since Iceland became a sovereign state in 1944. With a population of about 230,000, Iceland is a mini-state in many respects. But underwritten by the United States, it manages to play a full part in European councils--while protecting with vaunted Nordic vigilance its distinctive national character.

These unique and deliberately unsung Icelandic-U.S. ties were refurbished last week when Vice President Bush visited Iceland for talks on security issues with the country's leaders. He also took time to give a rousing pep talk to the 3,000 American military personnel and their families stationed here at the U.S.-maintained NATO base situated on an uninviting, wind-swept plain of volcanic lava.

To coincide with the Bush visit, the United States and Iceland signed an agreement for construction of a new civilian-military air terminal at Keflavik with about $20 million authorized by Congress. The go-ahead for the project is evidence that periodic efforts by Iceland's left-wing political parties to evict the United States have, for now, plainly been abandoned.

In 1974 an Icelandic government invoked the cancellation clause in the defense agreement that was signed with the United States in 1951. But the crisis subsided--in large part because of a petition signed by a quarter of the country's population opposing the move--and succeeding governments of various political casts have left the subject pretty much alone.

"The base as the U.S. presence is invariably styled is no longer an issue in Icelandic politics," said Styrmir Gunnarsson, editor of Morgunbladid, the country's leading newspaper.

There are several reasons why that is the case. Probably the most important is that given its size and resources, Iceland simply could not mount a meaningful defense of its own and has no desire to replace U.S. forces with anyone else's.

"No independent country wants a foreign force on its territory," Prime Minister Steingrimur Hermannson said in an interview, noting in an analogy often used here that the 3,000 American military living less than an hour's drive from the capital of Reykjavik is, in Icelandic terms, the equivalent of about 3 million foreign troops being stationed in the vicinty of Washington. But, said Hermannson, ask Icelanders whether they would prefer another national force to Americans, "perhaps Germans, French or even Scandinavians, the answer would be absolutely not."

Recognizing that national sensibilities are the major cause of Iceland's ambivalence about the American presence, the United States goes to considerable lengths to restrain its visibility. Only one U.S. flag flies at the base, out of sight of civilian traffic. Visitors to the U.S. Public Affairs Office get a slide show narrated in English but by a voice with a distinctly Icelandic accent.

Off base, no uniforms are permitted and there is a "downtown" curfew for younger enlisted men. The towns of Keflavik and Reykjavik have none of the honky-tonk bars and brothels designed to appeal to American tastes that are featured outside other U.S. installations around the globe.

In the mid-1970s, television service for the base was made closed-circuit cable so that its stream of American programming would not represent a major cultural invasion. Iceland takes such matters very seriously. Its national television channel is dark on Thursday nights to encourage citizens to attend concerts.

All in all, the U.S. presence in Iceland is as discreet as the Americans know how to make it. Any other stance would be disastrous. Suggest teasingly to an Icelander that his country is a bit of a banana republic, sort of like Panama was before it demanded back the canal, and the reaction is humorless and sharp.

There are no big U.S. commercial interests in Iceland, Bjorn Bjarnason, a columnist with Morgunbladid pointed out. "We have a defense and trading relationship with the U.S. that benefits us both," he said. "But we are culturally a European nation with a history of over 1,000 years. We have no inferiority complex in Iceland."

But while the United States does its best to be ignored, the Soviet Union has adopted exactly the opposite tack. According to the figures kept by naval intelligence, the number of Soviet planes and sea vessels sighted in and above Iceland's frigid surrounding waters has been rising steadily. The biggest upsurge has been in submarine operations.

"The growth in Soviet submarine deployments is awesome," Keflavik's commander, Rear Adm. Ronald F. Marryott, told an Icelandic audience recently.

During a 10-year period, he said, the number of Soviet nuclear-powered submarines passing Iceland has increased by about 300 percent.

Numbers such as those designed to justify American involvement have to be taken on faith. But there is no doubt about the growing size of Moscow's diplomatic contingent in Reykjavik. The Soviet mission is by far the largest in Iceland, with more than 80 people, more than four times the number of Americans at the U.S. Embassy.

The Soviets are buying up so much prime downtown real estate that a public drive is underway to stop them. Moscow's ambassador is a diminutive, cheerful fellow who chuckled in a chance restaurant meeting about which country is ahead in the ongoing Soviet-American competition for influence.

Moscow's most important hold on the Icelanders is that it sells them about 60 percent of the oil they need. While that amount has been declining recently, it still represents considerable economic leverage.

Overall, the record of U.S. relations with its military clients in recent decades has been unstable. Sometimes, as in the Indochina cases, tragically so. But in Iceland, there appears to be widespread recognition for now that the Soviets need to be countered in the North Atlantic and that only the United States is capable of doing so--under the internationalist guise of NATO.