ULAN BATOR, Mongolia (AP) _ Mongolians are showing resentment of the generations of domination by Moscow that began when their country followed the Soviet Union to communism in the early 1920s.

Growing anti-Soviet feeling is expressed in many ways, from heated exchanges between Mongolian journalists and Soviet diplomats to a hissed ''Russkie 3/8'' when a Mongolian driver mistook an American for a Russian.

Soviet influence has been strong since the founding of the Mongolian People's Republic. When its two neighbors, China and the Soviet Union, parted over ideology in the 1950s, Mongolia sided with Moscow.

A foreign reporter who had spent five years in the Soviet Union described Ulan Bator, Mongolia's capital, as ''a typical Russian town.''

The Mongolian language is written in Cyrillic, the same script as Russian. Nearly all educated Mongolians speak Russian and almost all intellectuals studied in the Soviet Union, which has put a great deal of money into the vast pastoral nation of only 2 million people.

Ulan Bator's debt to Moscow has been estimated by Western economists at the equivlalent of nearly $6 billion.

In recent years, Mongolians have begun emerging from the Soviet shadow. Nationalism, which sometimes takes the form of anti-Sovietism, is growing.

Mongolia revised the words to its national anthem last week, returning to original lyrics that do not mention the Soviet Union, according to the Communist Party newspaper Unen.

Unen means ''truth'' in Mongolian, as Pravda, the name of the Soviet Communist Party daily, does in Russian.

Primary schools began teaching traditional Mongolian script two years ago, and Mongolian adults who never were taught to read or write their own language are learning.

A youth of high-school age who cheered the removal of Ulan Bator's last statue of Josef Stalin last week spoke of ''the renewal of our national feeling.''

Among the demands of new political groups are withdrawal of the estimated 60,000 Soviet troops stationed along Mongolia's border with China and removal of the approximately 50,000 Soviet specialists and their families.

On Friday, the Kremlin said all troops would be out by 1992.

A foreign observer in Ulan Bator said the anti-Soviet sentiment was ''not explosive,'' but Mongolians ''resent the cultural hegemony.''

Resentment was obvious last week in the conduct of Mongolian journalists during a news conference at the Soviet Embassy on economic cooperation.

They bombarded Ambassador Vasily Sitnikov with questions on topics ranging from how Mongolia's debt to the Soviet Union would be calculated to why Soviet specialists in Ulan Bator built a wall around their living area.

Journalists took the microphone to accuse the Soviets of victimizing Mongolia by bartering or trading soft currency for its natural resources, and of buying Mongolian products at prices below the world market.

Comecon, the Soviet bloc's equivalent of the European Common Market, decided last year its members will begin trading in hard currency, at world prices, on Jan. 1, 1991.

Sitnikov told the news conference: ''The Soviet Union will give aid to Mongolia, which finds it difficult to enter such a Comecon system.''

Many Mongolians say their country will fare better under the new system because it will get better prices and hard currency for its gold, silver, copper, uranium, coking coal and other resources.

D. Surenjav, an economist and editor of the journal Economic Education, rose to the cheers and applause of colleagues to declare that, in reality, the debt was owed by the Soviet Union to Mongolia.

Surenjav argued in the January issue of Economic Education that the value of natural resources Mongolia has ''shared'' with the Soviet Union exceeds the amount of money the Soviets have invested in Mongolia.

He also claimed the Soviet Union has taken over border territory that includes some of Mongolia's best lands.

Some journalists asked why so many Soviets were in Mongolia doing jobs they said Mongolians could handle, and being paid twice as much. Sitnikov responded with irritation that working in Mongolia was ''not so prestigious'' for a Russian.