Romanian defector Bela Karoly, the gymnastics trainer who coached Nadia Comaneci to Olympic immortality at Montreal in 1976, will find it difficult, if not impossible, to repeat his Romanian successes in this country, according to American gymnastics officials.

His main problem: money.

"He's not going to be able to do in the United States what he did in Romania," said Don Peters, a friend of Karoly and the head coach of the Southern California Arco Team, one of the leading private gymnastics clubs in America.

"In Romania he had a system where the government sponsored everything and paid for everything. Nobody helps you here. The biggest problem any gymanstics coach has in the United States is finding the money to run his program."

Karoly and his wife Marta, both 38, informed Romanian officals Tuesday they are seeking political asylum in America, leaving behind a 7-year-old daughter in Romania. Joining them was Geza Pozsar, 31 a gymnastics choreographer who left behind a wife and infant daughter. Their decision to defect came at the end of a four-week tour of the United States, including a March 28 appearance at Capital Centre.

Yesterday, Rep. Bill Archer (R-Tex.) forwarded a letter to the Romanian Embassy calling on the government in Bucharest to expedite the exit visas of the defectors' families. The letter was signed by 13 members of the House Ways and Means Committee's trade subcommittee, which annually reviews Romania's most favored nation trade status with the United States.

There was no immediate comment from the Romanian Embassy but, in the past, relative of defectors have been permitted to leave the country.

In an interview shortly after their meeting with the Romanian officials, the Karolys and Pozsar said they hope to continue coaching in America. They left Romania, they said, because of repeated interference with their program by the government.

But it was generally agreed yesterday that without access to substantial funds, the three would find it impossible to establish their own gymnastics program in the United States, although they would have little difficulty findling jobs in the burgeoning U.S. gymnastics market.

Cost of equipping a facility were extimated at $200,000, and that does not include the monthly rent, salaries or other costs of operation.

In California, Peters says his annual budget is $500,000. He figures it cost $10,000 a year for each of his 30 competitive gymnasts when coaches' salaries ($18,000-$20,000) and travel costs are included.

"We run gymnastics classes for 800 kids for the luxury of being able to compete with 30," said Peters, who also does a limited amount of fund raising.

"They have an ideal kind of setup in Romania. The kids live in the gymnastics school. They get up in the morning and do some excercises. Then they go to class with special tutors, and then they have more gymnastics. Amateur sports is a national priority over there. I've known other Romanian coaches who have defected. They find out about amateur sports in the United States and it leaves tham almost shellshocked for about a year."

There are also other differences between gymnastics in Romania and in the United States, said Rich Kenney, a spokesman for the United States Gymnastics Federation.

"In a place like Romania the coaches and staff basically recruit the kids out of kindergarten. They watch them on the playground, and then they test them, and if they're accepted it's a great honor. In the United States we have to hope the talent walks in the door."

"Karoly and Nadia Comaneci (who won three gold medals and seven scores of 10 in gymnastics at the Montreal Olympics) were the people who put Romania on the map. He was the guy at the top. Things had to be pretty bad for him to defect," said Kenney.

Karoly's defection is also something of an embarrassment to the U.S. Gymnastics Federation, Kenney said, because it sponsored the Romanian tour. "It makes it look like we stole him," Kenney said.