Hirshhorn Museum curator Howard Fox, 38, a major force in the contemporary art scene here, will leave Washington in June to become curator of contemporary art at the Los Angeles County Museum of Art.

The move is yet another sign that museums in Washington and Los Angeles are racing to lead American cities in institutional involvement in contemporary art, while New York relies increasingly on its commercial galleries to keep up to date. Of the L.A.-D.C. rivalry, Fox says: "It will be a war of friendly rivals. We've both reached critical mass, so the competition between the two contemporary art scenes could be the greatest in the world -- a competition in perpetual overtime."

He joins the ongoing migration of Washington art museum professionals to Sunbelt institutions that includes not only his new boss, L.A. County Museum director Earl A. (Rusty) Powell III (formerly of the National Gallery of Art), but also E.A. Carmean, Peter Marzio, Walter Hopps, Jan Muhlert and many others who have left for the Southwest over the past few years. Earlier this month, it was announced that Victor I. Carlson, curator of prints and drawings at the Baltimore Museum of Art, has also been spirited away to become senior curator of prints and drawings at the burgeoning Los Angeles County Museum, starting in April.

Fox joined the Hirshhorn staff as a research assistant soon after the museum opened a decade ago, and rose to associate curator in 1982, acquiring a national reputation for original, thought-provoking shows that attempted to pinpoint and assess underlying trends in contemporary art. His "Directions" show in 1979 was the first -- and best -- of what has become a biennial series; and his "Metaphor: New Projects by Contemporary Sculptors," was a daring show of specially commissioned works by leading site-sculptors Alice Aycock, Siah Armajani, Dennis Oppenheim, Robert Morris, Vito Acconci and Lauren Ewing. Most recently Fox was coorganizer, with Miranda McClintic and Phyllis Rosenzweig, of the Hirshhorn's acclaimed 10th anniversary show, "Content: A Contemporary Focus 1974-84."

"Howard was the youthful spirit of the Hirshhorn," says retired Hirshhorn director Abram Lerner. "He brought the contemporary scene into the museum, and was hired for that purpose. He is very perceptive about the new art, very sympathetic to its aims, and consequently has a better understanding of what's happening than most curators. That's why L.A. wants him. He is also one of the sweetest human beings I've known in the profession."

Unlike many contemporary curators here, Fox also distinguished himself for his deep involvement with the Washington art scene, notably the Washington Project for the Arts, which he has served as a board member since 1980, and, in 1983-84, as chairman of the board. He was also art editor of Sun & Moon, a quarterly journal of literature and art -- now transformed into a publishing house for books on contemporary poetry, fiction and criticism -- founded by Douglas Messerli in Washington in 1976. Fox says that Messerli, his companion of 15 years, will move the Sun & Moon press to Los Angeles.

Fox's domain will be considerably enlarged by the move. The Los Angeles County Museum is currently building a new four-story structure, the Anderson Gallery, which will include 100,000 square feet of temporary and permanent exhibition space for 20th-century art -- more than the Whitney Museum of American Art in New York. He will have responsibility not only for organizing exhibitions, but for developing the growing collection of contemporary art -- which the museum defines as art from the last 10 years. He will report directly to the director, but will technically be part of the department of 20th-century art, whose senior curator is Maurice Tuchman.

"We wanted the best and most experienced curator in the contemporary art field around," said Powell of the appointment, "and we were extremely pleased that we could attract Howard to Los Angeles now, as the museum expands and the city expands as an international cultural center. He's a provocatively exciting curator for an exciting city."

No successor to Fox is likely to be named, "at least for a while," according to Hirshhorn Museum director James Demetrion. Rosenzweig, the associate curator, will continue to devote most of her time to contemporary art.

Says Demetrion, "It's a tremendous loss not only for the Hirshhorn, but for the Washington art community, and an indication of the esteem in which Howard is held in the contemporary art world. It's also a further indication that federal museums have a difficult time competing with museums in the private sector so far as holding on to their employes is concerned."