ALBANY, N.Y. (AP) _ Moscow's Musical Theater for Children has taken its show on the international road and is playing to rave reviews from the junior set here in the second half of a cultural swap with the Soviet Union.

''I think it was great,'' fourth-grader Michael Stefanik, 9, said this week after watching members of the troupe perform the ballet ''The Bluebird.''

Others in the crowd of 900 who attended the premiere, including a class of second-graders, practiced saying ''spasebo'' - ''thank you'' in Russian - to greet the cast after the show.

The Soviet company, and its leader, Natalia Sats, 82, who founded the world's first children's theater, are visiting upstate New York to repay a visit to Moscow in January by the Albany-based Empire State Institute for the Performing Arts.

''I have admired her work and her theater is incredibly beautiful,'' institute producing director Patricia Snyder said of Ms. Sats. ''It's just like a little palace for children and what happens inside the theater is also wonderful.

''When were were there (Moscow) in January, they made us feel that it was our home.''

Though plans for the exchange had been in the works for years, it was finalized after a cultural exchange agreement last November at the Geneva summit between President Reagan and Soviet leader Mikhail S. Gorbachev.

''Just as we were happy to send artists of the Empire State Institute for the Performing Arts to the Soviet Union as a gesture of our warm feelings to the people of the Soviet Union, we are honored to have these outstanding artists in our midst,'' Reagan told Snyder in a telegram this week.

The Soviet theater company is performing several different shows, including, ''The Bluebird,'' which is known as its signature piece. The music was composed by Ilya Sats, Ms. Sats' father.

The company is also to perform an opera and ''Peter and the Wolf,'' the children's piece that was written for Ms. Sats by Sergei Prokofiev in 1936.

All Albany performances of ''Peter and the Wolf'' were sold out before the company's performance Wednesday.

The Musical Theater for Children was founded in 1965 by Ms. Sats. She had earlier founded the world's first dramatic theater exclusively for children, the Moscow Central Children's Theater.

Soviet children are exposed more to theater than American younsters, said Ms. Sats, whose entire musical company numbers about 500. She has brought about 96 members to the United States.

''They say that it is nowhere that the children are so quiet and as moved as in our theater,'' she said. ''I never say in our theater to children 'Be quiet. Don't speak.'''

''What is most important in our theater is that our children are growing up together with our theater,'' said head choreographer Boris Lyapaev.

Dancer Igor Chirkov, a 13-year veteran who was greeted by children with drawings and gifts after his performance in ''The Bluebird,'' said the response of children in other countries to the theater is similar, ''though the Italian children are very, sort of, passionate.''

Later this month, members of the troupe are to perform in Minneapolis for four days.