She is a fourth-generation Bulgarian bareback acrobat and a proud member of the Girl Scouts of America. Her name is Stefka Slovova, known as Steffi.

When she fell last year from the shoulders of her father, Angel Slovov, who was standing on the back of a dray horse galloping around the center ring of the Ringling Bros. and Barnum & Bailey Circus in Madison Square Garden, she was knocked unconscious and was rushed to a hospital. That was when she was 11 years old. Now she is 12, and her act has been elevated one man higher.

She has bony knees and an exquisite fidgety politeness, but under her kid's face the bones are already arranging themselves into what will be a great eastern European beauty of the next decade. She was born in Sofia, and her parents came to America when she was 13 months old. There was never any question of whether she would join the Slovovi Troupe.

"When she was a little girl, she gave us no choice," said her mother, Margarita. "She would cry if we didn't put her on a horse."

When she is not doing tricks on horses with the 10-person troupe, Steffi lives with her parents in one car of the 42-car circus train. To get to Washington from Cincinnati via Charleston, W. Va., last week, the train ran all night, 525 miles for 19 hours, carrying 20 elephants, 19 tigers, six camels, four zebras, several hundred circus people and Steffi.

She goes to school on the train, too, in a special car where she is tutored in English. Because she usually works two shows a day and three on Saturday, sometimes she only has an hour of school. Between performances she receives further instruction from her mother. It is necessary to pay attention, because each year she returns home to Sofia for 30 days of intensive study in math, chemistry and history, followed by the mandatory Bulgarian state examinations. She has never failed them, "because if you do, you have to do the whole year over."

In Charlotte, N.C., where the circus stopped a couple of weeks ago, the Slovovi were seen backstage munching Girl Scout cookies. This was seen as a grand gesture, insofar as Steffi's grandmother, Angel's mother, is known as the greatest cook in the Blue Unit of The Greatest Show on Earth, and she makes cookies, too.

How Steffi came to join the Girl Scouts: "In one town, a lot of children came to the show with their teacher, and afterwards they invited me to," she said.

What town was that?

"What town was that?" her mother repeated helpfully.

"I don't remember," said Steffi. "It was a town last year."

Steffi does not have a complete uniform, only the green sash.

"She took it with her to school in Bulgaria," her mother said, "and all they were talking about was the Girl Scouts, and she was telling them about America. It was really fun for her."

Steffi nodded. Out of the corner of her eye she saw some other circus kids playing behind a pile of balloons. In the background, the show was going on, clowns were walking past, jugglers practiced. But Steffi sat still, on a clown box next to her mother. At 12, a girl is often dutiful and loyal and close at hand. Margarita and Stefka, mother and daughter, are best friends, and Angel is a father who, if you are good, will teach you a new trick on the horses.

To be a 12-year-old girl in the circus is to wear a rhinestone-studded costume and white leather boots and even some makeup, and (partly because you are 12) to be a star; and then, back on the train, to watch "Love Boat" and "Charlie's Angels" and "CHiPs" and "As the World Turns" with Grandmother as she cooks delicacies wrapped in grape leaves. Outside, America whirls past the windows, defining itself in new switching yards and armories week by week, but inside the Slovov family remains the same, still together after four generations.

There are 28 children in the circus, and Steffi is known as one of the responsible ones. She is called in if the other circus kids get out of hand. They listen to her. On the train, she cleans her own room. She cleans her own room?

"Yes, sure," said Margarita. "She has a problem with her little sister, Edith, who's 5, and who's not so neat. Steffi does the dishes, too."

"I wish you'd let me cook," said Steffi, looking up.

"Plenty of time for cooking later on," her mother said.

As for the accident last year, Steffi doesn't remember much about it. "I woke up after the X-rays," she explained. "I don't remember, so that's why I wasn't scared, I guess."

The family was petrified. Injury is always possible for circus people. Late at night in a nameless town when the sound of a distant siren is heard, performers look warily at one another. During performances of the riskiest acts, knots of colleagues gather in the corners of the arena. They watch, even though they have seen the routine a thousand times before. They know who has a sprained ankle, or the flu, or who just received bad news but is going ahead anyway with a stunt that relies for its success almost entirely on mental and emotional clarity. When an accident does happen, that's what they call it--an accident.

"When she had her accident last year they were doing a two-man high, she and my husband," said Margarita. "A two-man high, for them, they always feel sure. They never miss it. That's why there was no mechanic safety harness . But the horse got scared of something and stopped short, and they both flew off. She was lying there unconscious! We were so scared, oh God, we couldn't find our way out of the ring."

Margarita and Angel rushed Steffi to a local hospital, still in circus costume and makeup. Others who were there saw a scene of tremendous emotion, parental panic compounded unfamiliarity with American hospital procedures and traditions (previously, when a young clown sprained his ankle, Grandmother Slovova had wrapped it in onions). "The act continued, though," said Margarita. "Her grandfather, Doncho, still doesn't remember how he ended it. He doesn't know what tricks they did, or anything, he was so scared."

Steffi had suffered a concussion, from which she recovered completely. Now she does a three-man high.

"It's harder, the taller you get," Steffi explained. "Already, if I move just a little bit, we fall. Now I'm trying to learn to do a walkover, on the same horse. It's very difficult. It's sort of a forward somersault." Her father, she said, is a patient teacher. "But when he's hot he says, 'That's not right!' And I have to do it over and over again."

Her mother watches her grow up, aware of what lies ahead.

"What will happen to her is what always happens in the circus, especially with girls, sooner or later," Margarita said.

The 12-year-old looked at her mother, half curiously. At 14, when this topic arises, she will look with full curiosity; but for the moment, she still had one eye on some other kids nearby.

"She will want to make her own family," Margarita went on. "She'll stay in the circus, I'm sure of that. But some day she'll marry a performer and go and work for him. Or maybe if he's a bareback rider, he'll come and work for us. She's got a boyfriend already, a flier. And now she wants to practice the flying trapeze."

The flier was named. He is older than she, and it may be that he is hardly aware that she exists. But what he does is the most beautiful and glamorous of all the circus acts. She has watched him soaring above the ring, learning from his father, how to fly and fall and bow to new audiences in new towns.

Steffi looked uneasily at her mother. She seemed uncomfortable at this turn of the conversation.

Later, a clarification was issued by Stefka Slovova through official channels: While it may be true that a certain trapeze artist is of a certain interest to a certain bareback-riding Girl Scout, the trapeze artist does not have a name, or if he does, the name is not to be revealed.

Margarita was remembering what it was like to be from a family of fliers. Her father had a trapeze act when she was a girl, and she was in it. "He's 77 now, and he retired long ago," she said. "He always wanted me to marry a flier, and bring some new blood into our act. But what happened was I married a bareback rider instead, and left my father to join him." She was clearly pleased with her life--a life in which for 10 years, purely as the result of their circus skills, she and her family have been able to travel and live in the United States of America, returning home each year as celebrities. "I can't see myself in one place, really," she said dreamily. "I think it's basic for me, being in the circus."

The distant music changed, and Margarita jumped up from the clown box. "That's our cue, Steffi,we must dress."

"It's shorter this way," said the girl, starting south toward their dressing room on the other side of the Charlotte Coliseum.

"No, this way," said her mother, moving north toward the same dressing room.

"I'll beat you," said Steffi, dashing off in the middle of goodbye.

Tomorrow: The quadruple somersault on the flying trapeze.