WHAT MUST it be like for Laura Alonso to carve a dance career in Cuba when her mother is the celebrated Alicia Alonso?

And especially what is it like when she works for the Ballet Nacional de Cuba, which opens a three-week run at the Kennedy Center on Tuesday, and her mother is director, a principal choreographer and its prima ballerina?

Last week the younger Alonso stopped over her as the company was traveling from Dallas to Boston and discussed her life, her mother's and the appearances here of the Ballet Natioanl.

At one point in the interview, Laura seemed to confirm her mother's reputation as a patrician precisionist in Castro's Communist Republica de Cuba. Asked how Alonso runs the company, her daughter blurted with a mischievous smiles, "Well, she has full responsibility for what we do and who does it. Of course, she has a board of persons within the company to advise her on such matters. And then after that she does what she wants."

Certainly Alicia Alonso is granted her perks in the socialist state. There is her splendid home in residential Miramar, and her state car with chauffeur to take her on the 30-minute drive to the Garcia Lorca Theater in downtown Havana. "There was once a slight difference of opinion shall we say, on exactly how long it took," explains Laura in the same slightly barbed tone, "so we timed it to see who was right."

But Laura understandably jumps to her mother's defense on the matter of the car. "With her damaged vision, she is not safe behind the wheel. After the operations in 1972 improved her sight, mother tried riding a bicycle, but because of her remaining tendency to head toward a moving object (not such a disadvantage in a pas de deux) she drove right at a man who was walking in the street and he had to climb a tree."

At 40, laura looks much like her almost 60-year-old mother - the black hair, the arched brows and the high cheekbones. "It's just about the same, except that I have my father's nose and mouth." And when a photographer arrives, Laura intervenes with some of her mother's manner. "Stop," she declares, "I must put on my face. This is my early-in-the-morning face. They woke me too late this morning, and I had to rush to get a plane."

She becomes especially animated when discussing her mother's life and work. "She is not only a great dancer but a beautiful person as a humand being with a fantastic sense of humor. And then there is her choreography. Her new full length 'Swan Lake' we are bringing to Washington is going to be a surprise. I won't give away the details, but she goes from Act III into Act IV without an intermission, and in the process condenses the last act".

Their relationship seems to have changed and deepened in recent years. The long separations when Laura was being schooled in Cuba while her parents danced abroad are long past. And the years when Laura was overshadowed as a dancer by the superstardom of her mother ended when Laura had to quit because of diabetes. ('I simply didn't have the strength") Now, in her new role as a maitresse de ballet for the Ballet Nacional, she seems to have thrown off any feelings she might ever have had of subordination to the Great Alonso.

"I did some work with her soon after I started teaching for the company, and then on my birthday she called and said, 'I've decided you're going to teach me just as I taught you. When I am dancing, I cannot see adequately in a mirror. You are going to be my second eyes.'"

Has it worked? "Very well," asserts Laura, getting up from her sofa and raising one leg into an arabesque. "This leg can always stretch a litter farther," she notes, "and like every other dancer, mother needs someone who can see it."

Meanwhile, Laura and her second husband, cinematographer Levio Delgado, have moved to a home "around the corner from mother, because it is easier that way."

Told that her English is amazingly fluent for someone who, like her mother, was barred from this country for 15 years because of strained relations between the two countries, she replies, "Well, would you believe that I was born in Manhattan?" It was at American Ballet Theater that Alonso built her legendary reputation over the '30s and '40s. "In those days, most Cuban dancers had to leave to make careers. That was particularly true of the men like my father [Alicia Alonso's former husband, Fernando, Alsono]. If they stayed in Cuba before the revolution, they had to make what they could in the clubs.

"With Castro coming to power, my parents returned; and with the generosity of Fidel, our company was put together." He started it with a $200,000 subsidy "if we could put together a company of international rank. Now we depend entirely on state money and the box office, where tickets are $1.50."

Asked if such success for the company would have been possible without the Alonso, their daughter replied discreetly, "Well, let us say it was done quicker because of them."

When Alonso returned triumphantly to New York four years ago as the unannounced star of an American Ballet Theater gala, Laura came too. It was a homecoming for them both, because Laura had spent so much of her youth there.

"We hadn't seen Nora Kaye in years except on tours in Europe and places like that. And also there was Igor Youskevitch [Alonso's longtime partner] and there was Royes Fernandez [another famous ABT dancer], who used to barge in and grab my fried bananas from me when I was a child. And there was my very, very best friend. Bambi Lismore, whom I had last seen when she was the godmother at the baptism of my son [Ivan Moreal, who at 20 now dances with the company]. For years, I couldn't even reach her by phone. It was after the revolution, but I decided to have a church ceremony anyway, because the two grandmothers both were suffering from cancer, and they felt a need for it. In Cuba, the cuurch is not such a force now. But some people need the church, like you need a doctor.

She recalled the early days. "Mother was in a show and the star, I think, was Ethel Merman and she let me play in her dressing room. I dropped things and emptied the perfume bottles and broke things, but no one complained. And on stage during rehearsals, they would keep me busy by giving me a ballet shoe and some alcohol with which to clean it. I think it's important for a child to feel busy, to feel like they are doing something that's worthwhile, don't you?"

Being a mother is not always the easiest thing for a dancer. And leading ballerinas who have children are very much the exception. The frequent strains between ballet stardom and motherhood is the central theme of the movie "The Turning Point," a copy of which filmmaker Herb, Ross and his wife, Nora Kaye, the executive producer, carried along recently to Cuba, where they went to visit Kaye's old ABT colleague, Alonso.

Laura particularly admires the dance sequences with Leslie Browne and Mikhail Baryshnikov. But she argues that the central theme does not "apply" to socialist Cuba.

Soon after, though, she is taking about how both she and her mother married dancers when they were very young and how both marriages ended in divorce. "Mother discouraged me from going into dancing," adds Laura, "because of the rigor and confinement of a dancer's career. She wanted me to have a different life."

Freedom from the limit of dancing herself has given Laura time in recent years for a second career - teaching dance as therapy for an experimental school in Havana for children with physical and emotional disabilities. "They had approached mother about it, and she encouraged me to do it instead of her."

The company is now going at full tilt, with 167 members - 85 of them on this tour,with six Washington premieres alone.

But the inevitable question arises about the possibility of Alicia Alonso's retirement. According to Laura, "Every once in while she uses a phrase like 'When I retire' and we all grab our brows in dismay and tell her, 'Please don't, for our sakes. You've got so much energy and determination now, what would you do with it if you didn't go on?'" CAPTION: Picture, "Mother wanted me to have a different life." By Harry Naltchayan - The Washington Post