The three Romanians who discovered and trained superstar Nadia Comaneci remained in seclusion yesterday in California, following reports that another gynmast passed herself off as Ecaterina Szabo, the European junior champion, during a U.S. tour this winter.

Reliable sources confirmed that the switch had taken place and was arranged by the Romanian authorities. But the Romanian trainers have refused to comment.

With their applications for political asylum pending in Washington, the three trainers are waiting to hear from the Romanian government about permitting their families to join them here.

The three trainers are Bela Karoly, 38, head coach, his wife and assistant coach, Marta, 38, and their lifelong friend, head choreographer Geza Pozsar, 31. State Department sources say that it may be more than a year before the Romanian government agrees to let their families come here. Left behind were Pozsar's wife, Maria, a French teacher; their infant daughter, Karina, and the Karolys' daughter, Andrea, 7.

Under federal law, it is a crime to knowingly aid or cause a person to enter the United States under an assumed name. Violators face deportation or a maximum of five years in prison.

The switch of gymnasts occurred during the Jan. 31-Feb. 1 International Gymnasticsd Classic in Los Angeles. NBC-TV sports had acquired television rights to the event at a cost said to be in the vicinity of $150,000. Part of the agreement was that Szabo, sometimes described as the gymnastics heir to Comnaeci, would be part of the Romanian team.

But, in fact, Szabo did not participate in that event. Another gymnast, believed to have been Lavinia Agache, performed under Szabo's name. A month later, on a tour of the United States that included an appearance at Capital Centre, Szabo did participate.

The three Romanian trainers reached their decision to stay in the U.S. around 3 a.m. on March 30, after a four-week tour by the Romanian women's gymnastics team. The three walked out of their hotel in New Ork shortly after noon, as the rest of the delegation was out for last-minute shopping. They took a taxi to midtown Manhattan, where Marta Karoly's 75-year-old aunt put them up in her efficiency apartment. Drained of emotion, they watched television, keenly aware that at 4 p.m. their team was to assemble for the trip to the airport. They had not said goodbye to anyone.

A few minutes after 3 p.m., news of the attempted assassination of President Reagan reached the incredulous Romanians. As they tried to apply their few words of English to the drama, they kept saying, "Good God, what a time we chose to come here." But there could be no turning back. They did not call the team or Romania's national airline, Tarom, which kept its plane on the tarmac at Kennedy International Airport for three hours in case they might appear.

They tried to phone their families in Romania, but the phones there had already been disconnected.

Advised by friends, they filed for asylum with the Immigration and Naturalization Service. The following week, they flew to Washington and went to the offices of attorneys Alan Rothenberg and Carol Critchlow, who offered to represent them free of charge.

There was to be a confrontation, albeit a ritualistic one, arranged by the State Department. The signs seemed favorable. In 1980, the number of Romanians allowed to emigrate to the United States went up to 2,800 from 1,500 in 1979. But a waiting period of 14 months seemed to be the standard.On occasion, Romanian officials acted in a threatening way.

Refrain from showing emotion, cautioned tax attorney Rothenberg, 39. Present your case logically.

Pozar asked how to react if the Romanian official presented messages from their families appealing to them to return home. Don't rise to the bait, he was told. Be as calm as possible.

By the end of the session, Rothenberg learned the phrase "cool it" in Hungarian. "Nyugi, nyugi," he kept saying as he left for the State Department with his clients.

The meeting was attended by two Romanian diplomats, three State Department officials -- one an interpreter -- and a representative from the Immigration and Naturalization Service. The ranking Romanian, First Secretary Florin Dumitrescu, kissed Marta Karoly's hand and had a smile for everyone.

What are we going to say to 22 million Romanians who admire you? he asked the three trainers. He said he couldn't believe that such leading citizens would choose not to return home. And, incidentally, what if Andrea Karoly didn't want to come to the United States?

Bela Karoly explained that their decision was irrevocable and that it had to do with the Romanian Gymnastics Federation. As for daughter Andrea, she is only 7 and too young to decide, he said. He asked that the Romanian government permit Mrs. Pozsar and the two daughters to come to the United States.

Dumitrescu pointed out that he couldn't do anything personally; the decision was up to Bucharest. He shook his head in disbelief, saying that this incident would not have come to pass had the trainers informed the highest state authorities of their disagreements with the gymnastics federation.

According to the trainers, their feud with the gymnastics federation goes back to 1973, when their school's team astonished the Romanian sports world by winning all the titles in the national women's gymnastics competition.

The Karolys, classmates at the Higher ensitute for Physical Education in Cluj, Transylvania, began their careers in 1968 as physical education teachers in Onesti, then a new town of 30,000 east of the Carpathian mountains. Their innovation was to start training girls at age 7, instead of the usual 10.

"We were popular in Onesti," Pozsar said. "But in Bucharest, the gumnastics federation was jealous and reacted to our little girls winning in the national competition by restricting the adult competition to girls above the age of 14."

But the little girls were growing up fast. In 1975 in Norway, Nadia Comaneci, not yet 14, became the all-around European champion, beating the Soviet Union's world champion, Lyudmila Torischeva, 20. In the five categories, Comaneci won four gold medals and one silver.

With the Montreal Olympics approaching, Karoly called for a national competition to select the team. When the gymastics federation kept delaying action, Karoly went to the member of the party central committee responsible for the Olympics. Ilie Verdet, who has since become prime minister, promptly ordered a competition, which resulted in a sweep by Karoly's girls: out of six gymnasts, five came from his team, and he was appointed head coach. In Montreal, Comaneci became the absolute champion of women's gymnastics, and the Romanian team took second.

Returning home, the team was given a welcome usually reserved for victorious armies. Party boss Nicolae Ceausescu declared Comaneci "the ideal for Romanian youth." The gymnastics federation was not happy with the developments, Karoly said. It talked Comaneci and three of her teammates into moving to Bucharest, promised an apartment there for Comaneci's father, a car mechanic, and created tensions in Onesti.

After 10 years, the three trainers said they felt so harassed that they arranged for the transfer of their school to Deva, a town of 60,000, across the Carpathian mountains, in Transylvania. Thanks again to the intervention of party leader Verdet, Deva received the most modern gymnastics facilities. In a vast regional competition, the three trainers selected 500 girls and began coaching with fresh enthusiasm.

In Bucharest, Comaneci and her teammates lived a good life in a special sports hotel. In 1978, the Karolys' student, Emilia Eberle, 14, won the national and European championships. Comaneci, then 17, was overweight, slow and sloppy. She asked Karoly to take her back as his student. The sports council the organization with authority over the gymnastics federation, appealed to Karoly to prepare her for the world championships in Strasbourg.

"She is independent-minded and ambitious, but suggestible and with a weakness for money.We took her back. She was, after all, our student. We then tried to do the impossible: to put her in shape in four weeks before the competition," Karoly said.

In Strasbourg, Comaneci won in only one category and slipped to fourth place overall. "After Strasbourg, we took her with us to Deva, and it was like the old days again," Karoly says. "In less than a year, in 1979 in Copenhagen, she was again the undisputed champion of Europe."

In 1979, in the world championships in Fort Worth, Tex., the entire Romanian team was from Karoly's school. Although Comaneci was injured, the team won an unprecedented victory over the Soviets. "Our system of training was vindicated," Karoly said. "This was the greatest moment of our career." After Fort Worth, the gymnastics federation once more talked Comaneci into going to Bucharest. Then once again before the next competition, the Karoly team was asked to take her back.

"At the Moscow Olympics, the Russians did as they pleased," Karoly said. "When our girls perfomed, the Russians jeered and turned down the volume for the music so our girls couldn't hear it. We knew that the judges were told to give fewer points to our girls. We protested orally and in writing. The Russians rudely dismissed us, and their team won. Nadia won two gold medals, but came in second overall. She and our team deserved to be first.

"Thanks to TV, people could judge for themselves. Reporters reporting live agreed with us. But when we returned home, not a single Romanian official congratulated us, and the gymnastics federation called our performance unsatisfactory. The public thought we were great heroes because we stood up to the Russians. To our way of thinking, this not heroism. We did what we had to do as sportsmen: protest unsportsmanlike behavior."

The Moscow Olympics made it clear to the three trainers that politics set limitations to their professional ambitions. Their decision to leave Romania was clinched on the U.S. tour this March. They said the leader of the delegation, an official from the gymnastics federation, treated them like dirt.