American Ballet Theatre director Mikhail Baryshnikov wrapped his arm around First Lady Nancy Reagan backstage at the Kennedy Center Opera House after last night's gala performance and introduced her to his dancers.

"Nice to meet you," said Mrs. Reagan as she walked down the line. "You were all so good . . . Thank you so much for a wonderful, wonderful evening."

A photographer asked her to shake Baryshnikov's hand. She did, and exclaimed, "After we've been standing arm-in-arm, we go to a handshake!"

Asked by a reporter what she thought about her son Ron leaving his job as a dancer in the Joffrey Ballet, Mrs. Reagan smiled and said, "Whatever he wants to do."

Mrs. Reagan had been seated in the presidential box with friends Mr. and Mrs. Rawleigh Warner, Mr. and Mrs. Andrew Heiskell and C.Z. Guest, and they were joined by Baryshnikov after he danced in "Harlequinade." He lead the first lady backstage, where she talked with the dancers before returning home.

And when all the hugging and congratulations ended, many of the dancers and about 100 patrons went on to a post-performance party at Nora's restaurant.

There, Baryshnikov sat at the bar having a Pilsner and said that "sooner or later" he is going to reinstitute ABT's pattern of two Washington seasons each year.

"We're planning to come back" for the double season, he said. "I hope so. Next year we are coming for a big winter season . . . four weeks in Washington." The second season, in spring, was dropped last year, and this year the company is here for only eight performances. Its regular winter season was canceled because of a labor dispute.

At Nora's, Baryshnikov and his dancers hosted the small party in an effort to build a core of support here. "We've always had a home here, you know," said Baryshnikov, "but like to kind of extend the amount of people who are really interested to support us morally and financially."

"I just love this company, it's great," said 19-year-old Amanda McKerrow, the award-winning ballerina from Rockville who left the Washington Ballet only a short time ago to join ABT. "I'm learning so much. Did you like 'Duets?' " she asked, referring to modern ballet performed to music by John Cage last night.

"Great!" responded one of the several people huddled around talking to her.

"We never know how the audience will accept it," McKerrow said. "That is one of my favorite pieces."

Janet Solinger, director of the Smithsonian Associates program, sat at a table with Nat Aronson, an aviation consultant. "I never miss an ABT performance," she said. " . . . I think [the Smithsonian] is going to do some programs with the ABT next year. We would have people go to the performances and then have lectures on them later."

"I am a lover of ballet," said Aronson. "We've had such a poor year. It's just such a pleasure to see such dancing."

Walter Arensberg, an urban planner with the architecture firm of Skidmore, Owings and Merrill, said he and his wife bought the $75 special tickets that included last night's performance and party to help the ABT.

"I think it's very exciting," Aronson said. "I'm one of those people who believe that Washington has come alive in the last 15 years, and the more we can do to establish the ballet and theater and other arts on a solid footing the better."

Sharon Patrick, a New York management consultant and an ABT board member who organized the party, said, "I tried to get people who live and work in Washington" and who can be counted on later to help sell tickets and raise money for ABT.

Baryshnikov said dancer Gelsey Kirkland, who is back with the company after leaving and returning several times and who will be performing with it here Saturday night, is "coming back strongly. She's been rehearsing with us all the rehearsal season. She's starting slowly. She's in a good mood and good shape."

Baryshnikov said he regularly visits George Balanchine, whose "Symphonie Concertante" the ABT performed last night, in the New York hospital where Balanchine is being treated. "He's doing pretty well," Baryshnikov said. "We did this [performance of 'Symphonie Concertante'] just before his birthday Saturday: to pay him back with this performance . . . It was our present to him!"