A 30th anniversary review is under way of cultural exchange, a nice and seemingly quiet corner of Soviet-American relations, and the startling thing is how successful it has been and what it is becoming now.

The general view is that the exchange of musicians, scientists and the like, conducted in the name of serving mutual ''understanding,'' has had propaganda and intelligence value for both sides and should go on. But this understates the hidden American purpose, the actual Soviet result and, as we shall see, much more.

The American purpose was stated in a 1956 National Security Council directive setting up the first, Eisenhower-era exchanges. Yale Richmond got the text declassified and prints it in his''U.S.-Soviet Cultural Exchanges, 1958-1986: Who Wins?'' (Westview). ''To promote within Soviet Russia evolution toward a regime which will abandon predatory policies . . . ,'' exchanges would transmit facts, ideas of freedom, a taste for personal security and consumerism, and encouragement for nationalism in Eastern Europe.

A Cold War fantasy? Until recently few people expected exchanges to carry such a heavy society-transforming regime-altering mission. But Richmond, a retired State Department hand at cultural exchange, makes a strong case that the program's opening of a Soviet window to the West strengthened the currents that helped propel Mikhail Gorbachev to power.

Exchanges have stoked popular demand for a better life. Knowing this, Soviet reformers such as Nikita Khrushchev and Gorbachev have expanded the programs -- not just to skim Western know-how but also as a lever in struggles against Kremlin conservatives. Exchanges have also honed the elite's interest in applying selected Western ways to break through systemic stagnation.

Success, however, is reshaping exchanges. With Gorbachev and glasnost, Moscow is exploiting American openness more intelligently and boldly to pursue science and technology, to stroke the American peace groups and to mix with the mainstream in exchanges with Congress, the media and so on. The old clutch for control remains: the Kremlin still funnels most programs through a few official bodies. It let only 400 of its citizens spend more than a month here last year, compared with 20,000-plus Chinese. But some administrative flex is visible to our specialists and -- a sensitive index -- it's starting to let its people stay in private American homes.

The NSC directive of 1956 expressed a telling wariness toward exchange initiatives coming from the Soviet Union and from private Americans. These should be welcomed, the directive said stiffly, pairing them, ''whenever they advance U.S. policy or seem to be an acceptable and necessary price for what will advance U.S. policy. But the Government should be thinking and planning imaginatively in this field.''

For years, many private Americans, including liberal cultural and scientific figures who were proud champions of independence from government at home, lent themselves to the official exchanges. It was personally rewarding and it was for a good cause. This readiness to put culture and science in state harness was an important way in which we Americans became more like the Soviets -- this in a program whose purpose (expanding freedom) was to make them become more like us. Talk about cultural exchange!

But more recently the United States has seen an explosion of demand for direct citizen involvement in exchanges and contacts of all kinds. Harriet Crosby, co-editor of Surviving Together, a 5-year-old journal celebrating these mostly liberal private-sector programs, attributes them to Gorbachev's reform appeal and to Ronald Reagan's first-term nuclear negativism. ''American citizens, feeling their government was not doing enough to avert the threat of nuclear war, took matters into their own hands.''

Conservatives looking at this explosion are caught between a dutiful respect for the private sector and a rueful awareness that the Kremlin is playing to the American opposition. The standing that private individuals and groups gain from conduct of ''citizen diplomacy'' is already starting to clutter or deepen, whichever, official policy making. This new and uncharted development is what imparts a special tang to exchanges as they enter their fourth decade.