Alexander Godunov, a principal dancer in the world-renowned Bolshoi Ballet, was granted asylum in the United States yesterday.

Godunov, 29, the first dancer to defect from the Bolshoi, formally requested asylum Wednesday at the New York City district office of the Immigration and Naturalization Service.

His action came as the Bolshoi was in its fourth and last week of performances at Lincoln Center. The company is touring the United States with stops also planned in Chicago and Los Angeles.

Godunov's wife, Ludmila Vlasova, also a soloist with the Bolshoi, has not asked for asylum with her husband.

The State Department yesterday informed the Soviet Union officially about the asylum. Neither the Soviet embassy in Washington nor the Soviet U.N. Mission had any comment.

Despite earlier reports that the Bolshoi might cancel its tour, Lillian Libman, executive producer of Nederlander Producing Co. of America, the American sponsors of the Bolshoi tour, said she expected the tour to continue. Libman said the defection "came as a total surprise to the Bolshoi Ballet administration and the American producers, all of whom expressed their great regret at the action taken by Mr. Godunov."

Godunov, described by one dance expert as "a huge audience favorite" because of his "powerful dramatic" dancing style, was reported by the Associated Press to be "in private custody somewhere." The circumstances of his defection remained unclear.

One report from the New York dance community placed Godunov on a yacht near the city, perhaps with Mikhail Baryshnikov the dancer who defected from the Soviet Union in 1974. The two are friends and were classmates in Riga 15 years ago, before Godunov joined the Bolshoi as a soloist in 1967.

According to Gennady Smakov, a dance critic for Ballet News in New York and a former Soviet national, Godunov wanted to defect in 1974 when he was on an American tour with the Bolshoi.

"There were all kinds of rumors at the time," Smakov said yesterday. "But 'Sascha' couldn't do it. The KGB knew about it . . . I was surprised they let him make this tour. I don't know why they let him out of the country now."

Godunov joins other famous Soviet dancers who have defected including Baryshnikov, Rudolf Nureyev once Natalia Makarova -- all dancers once for the Kirov Ballet in Leningrad.

During the past year, the Bolshoi reportedly has been split by internal dissension. Some of the company's most famous dancers have openly criticized the artistic policies of chief choreographer and artistic director Juri Grigorovich, and those critics were conspicuously absent when the 125-member Bolshoi troupe arrived in America.

Among the principal dissenters is the Boishoi's prima ballerina, Maya Plisetskaya, with whom Godunov has danced many times. He was reported to have taken her side in the intramural feud, but later to have converted to Grigorovich's side.

Godunov, a gold-medal winner in the Moscow Ballet Competition in 1973, has played major roles in "Anna Karenina," "Love for Love" and "Spartacus."

One of the world's tallest ballet dancers at 6-foot-2, Godunov wears his long blond hair in a page-boy style. He is said to like crowds and accepts bouquets at curtain calls. He was the only Boishoi member met by a limousine after performances, though some said the limousine was used to keep tabs on him for fear of a defection.

"I'm very enthusiastic," Smakov said of the defection. "I think it's a big acquisition for American ballet. He has a big future here. He would be a perfect dancer for George Balanchine and the American Ballet Theater. He is a very strong classical dancer."

In The New York Times of April 20, Cynthia Gregory, principal ballerina of the ABT, was quoted as saying, "I wish Alexander Godunov of the Bolshoi Ballet would defect for me. I love his Prince Valiant look, and he's so exciting." Gregory, who is almost 6 feet tall, had sometimes complained that she wanted to dance with a taller partner.

Baryshnikov, who three months ago was named to become director of the ABT, is reported to have met with Godunov Sunday night, leading to speculation yesterday that Godunov might join that company this fall. According to sources in the New York dance community,Godunov is expected to make a public statement Monday about his defection.

Lucia Chase, current director of the ABT, said yesterday that the company "has not been in communication or in negotiation with Mr. Godunov. We know he is a wonderful dancer with superb Russian training, and I hope he will be happy in his decision."

A caller to United Press International In New York, who refused to identify himself, said yesterday that Godunov will rest for a while and then "seek affiliations with choreographers in the United States." The caller, claiming to represent Godunov, quoted the dancer as saying, "I am looking forward to broadening my experience and working in new areas of dance."

Under normal procedures, an applicant for asylum files a request with the INS and awaits a decision, which can take weeks.

A State Department spokesman said, however, that "Soviet defectors are special and unusual." Most Soviets who seek asylum claim that if they were to remain in the Soviet Union they would be subject to persecution for their political beliefs.

Gudunov is not known to have strong political opinions, but his request for asylum was granted almost immediately.

"The law makes it easy to grant asylum to people from communist countries," said Vern Jervis, press officer for the INS.