Jane Livingston, 34, has been named associate director of the Corcoran Gallery of Art.

Her promotion - she has been the Corcoran's chief curator since 1975 - involves additional administrative duties and reaffirms and exhibits at this city's oldest private art museum.

Doubts about her future here had circulated widely before the appointment of Peter C. Marzio as Corcoran director last May.

Livingston was waiting to see who would get that job. In addition she's been offered a tenured director's post at a New York state museum of comparable size.

"It was an agonizing decision, but I've made up my mind," Livingston said yesterday. "I'll be here for a while."

Old and nagging questions about who would run the Corcoran now appear resolved. A triumverate will be in charge. Associated director Livingston will be responsible for the gallery, its exhibitions, budget, and general art policies. Peter Thomas will have comparable independence as the dean responsible for the Corcoran School of Art. They both will report to director Marzio who will be in charge of fund raising and general administration, and will be the link of the Corcoran's trustees.

Marzio's field is 19th-century American history and art. Livingston's is the 20th century. Though Marzio is a museum professional with strong academic credentials, as the Corcoran's chief executive he will not organize shows.

Livingston, who came to Washington from the Los Angeles Country Museum, has earned a first-rate reputation here for her photography exhibits. She has arranged more than a dozen at the Corcoran since 1976. She has also given solo exhibitions to such local artists as Ed McGowin and the late Howard Mehring.

The Corcoran's new season will open in September with a retrospective given to the work of the Mexican photographer Manuel Alvarez Bravo. An area sculpture show, also organized by Livingston, will open in September. For the next Corcoran Bicennial, she has chosen to exhibit new work by such New York "old masters" as Willem de Kooning, Roy Lichtenstein, and Jasper Johns. A show of recent paintings by Frank Stella open next spring.