After weeks of speculation and sometimes conflicting rumors prompted by the illness of New York City Ballet cofounder and principal choreographer George Balanchine, the company's board of directors yesterday named Peter Martins and Jerome Robbins "ballet masters in chief" of the troupe.

The announcement, read to the NYCB dancers and staff yesterday by board president Gillian Attfield in a meeting described as "brief and low-key," also said that Martins, "in association with Jerome Robbins, will be responsible for the operation of the company."

The statement began by conferring permanent honorary status upon Balanchine: "To leave no doubt as to our love and respect for George Balanchine, we have named him ballet master emeritus." It also noted that Lincoln Kirstein, 75, who cofounded the NYCB with Balanchine in 1934, will continue in the post of general director: "Thus his artistic judgment and his dedication will continue to be invaluable to the company."

As a reason for the announcement, Attfield said in her remarks to the company: "George Balanchine and Lincoln Kirstein gave us the New York City Ballet, which today is one of the great cultural institutions of our time. For this we are eternally grateful. George Balanchine has been away from the company since last summer, and it is now clear that his illness is such that he will not return actively to the company."

Balanchine was present briefly in Washington when the NYCB appeared at the Kennedy Center last October, and was admitted to St. Luke's-Roosevelt Hospital in New York in early November. He remains hospitalized there, with an official diagnosis of "progressive cerebella degeneration." He is said to have good days and bad, but his condition has not changed dramatically over the past several months. Balanchine was 79 Jan. 22.

During Balanchine's illness, the company has been run primarily by Kirstein, Robbins, Martins and general administrator Betty Cage. Martins, 36, is a principal dancer with NYCB, which he joined in 1970 after a distinguished career in his native Denmark. He has also become prominent in recent years as a choreographer in his own right, and in 1981 he was named "ballet master" of the NYCB, until now the title shared by the company's artistic directors, including Balanchine himself, Robbins, Martins and John Taras. Martins, who also recently was designated artistic adviser to the Pennsylvania Ballet, had been widely rumored to be Balanchine's chosen "heir apparent." Robbins, 64, the notable choreographer and stage and film director (and in earlier years a dancer as well), has been associated with NYCB since 1949, and has enjoyed a close personal and artistic relationship with Balanchine over the years.

Under the new leadership arrangements, the company will begin a nine-week spring season at Lincoln Center's New York State Theater April 26. It is during this season that Leonid and Valentina Kozlov, the Bolshoi Ballet defectors just engaged by NYCB and seen here recently in the Kennedy Center's production of the Rodgers and Hart musical "On Your Toes," will begin dancing with the company. The spring season will be followed by a week's holiday, and then the annual three-week summer residency at the Saratoga Performing Arts Center. On Aug. 19, the troupe departs for a tour of London, Copenhagen and Paris, with two weeks in each city; returning to New York Oct. 3, the company starts a five-week rehearsal period. The NYCB's next scheduled appearance in Washington will be at the Kennedy Center Opera House from Feb. 28 through March 11, 1984.