PONTUS HULTEN is leaving Paris for the Sunbelt -- and when Pontus Hulten moves, the museum world takes note.

Hulten, 56, is bear-shaped, sharp-eyed Swede whose specialty is starting important and adventurous museums of modern art. He did it first in Stockholm in 1958 at the Moderna Museet. Then he moved to France to become the first director of the Centre National d'Art et de Culture Georges Pompidou, that glass-and-steel complex known as the Beaubourg.

Now he's taken a new job.

Hulten has agreed to organize, from scratch, a Los Angeles museum of contemporary art.

He was one of the first curators in Europe to show the art of Jackson Pollock, of Rauschenberg and Jasper Johns, of Oldenburg and Warhol. It is clear that Hulten senses art trends early. His decision for the Sunbelt means he's glimpsed another.

That land of palms and plenty is experiencing an art-museum boom.

The museums there are rich, confident, ambitious, hungry for Old Masters -- and most of them are new. For the first time, they are offering serious competition to their counterparts on the East Coast.

Because they're buying costly art and building costly buildings, gifted art professionals -- among them the directors of the Yale Center for British Art and the Husdon River Museum -- in recent months have been fleeing the Northwest and taking Sunbelt jobs.

"The Southwest is where it's happening," says collector Marcia Weisman, one of the trustees of Hulten's new museum. "It has been like an oil well' bubbling in the weeds. Now it's about to gush."

"No question about it," said Earl A. "Rusty" Powell III, who left Washington last winter to become director of the Los Angeles County Museum of Art. "You can feel this city pulse."

The new museums are spending lavishly, winning at art auctions rare, expensive pictures that not long ago would have gone to the East Coast. Their new exhibition spaces are luring to the West large traveling exhibits of the sort that a few years ago rarely dared to venture past the Mississippi. oThey are wooing away staff. And they are taking away patrons -- Sunbelt art collections, as well as Sunbelt monies, that once flowed toward the Northeast.

These developments and others in aggregate suggest that the center of gravity of the American museum world is, like so much else these days, being tugged toward the Southwest.

Millionaire collectors such as Kay Kimbell, Amon Carter and William Randolph Hearst have nourished the museums there. Other Sunbelt patrons -- among them men as rich as Armand Hammer, Coca Cola's Robert Woodruff and the late J. Paul Getty -- of late have been supplying the museums of the Sunbelt with huge amounts of cash and first-rate works of art.

When collector Norton Simon, who shows his art in Pasadena (and is Marcia Weisman's brother) recently acquired -- for $4.25 million -- a rare 15th-century painting, Dirk Bouts' "Resurrection," he did so by outbidding Britain's National Gallery of Art.When the famous "Icebergs" of Frederic Edwin Church sold recently at auction for $2.5 million, it was bought by Lamar Hunt, the billionaire from Texas. His Arctic panorama is now displayed in Dallas.

Hulten's new museum does not yet have a building or an art collection, but thanks to its trustees -- Eli Broad and Max Palevsky -- and to Atlantic Richfield, half of its projected $10 million endowment already has been raised.

Most Sunbelt museums are relatively new. The Los Angeles County Museum of Art received much art from Hearst in the 1940s, but only opened its large building in 1965. Norton Simon's grand collection is housed in Pasadena in a building finished in 1969. The Kimbell in Fort Worth, founded by Kay Kimbell, dates from 1972, and the Getty Museum in Malibu, a modern Roman villa, was opened to the public in 1974.

The architects responsible for the Sunbelt's new museums include some of the most distinguished designers of our age. Mies van der Rohe designed the one in Houston. Louis Kahn and Philip Johnson have built in Fort Worth. And four costly new museums -- one in Dallas, two in Los Angeles, and one in Atlanta -- soon will be constructed.

That is where the artists are -- and have been for years. Think of Diebenkorn and Wiley, Disney and O'Keefe. Sam Francis and Robert Irwin, two of the best of them, are among those organizing Hulten's new museum. Patron Max Palevsky says that "though Los Angeles has the second-most-important art community in this country, it has been invisible. That's about to change."

The European tourists who came here for the pictures 20 years ago headed for Manhattan, and except for side trips to Cleveland or Chicago, Philadelphia or Boston, they rarely left New York. Today they'd have to visit Washington as well, for the art museums here, many of them new -- the National Collection of Fine Arts, the National Portrait Gallery, the Hirshhorn Museum and Sculpture Garden, the National Gallery's East Building -- have combined to make this city a center of world art.

Twenty years from now, such picture-seeking tourists may also be obliged to visit the Southwest.

Consider these developments:

The Getty Museum, Malibu, is not yet, but soon will be one of the world's richest. Attorneys are still squabbling over its endowment -- estimated value: $750 million -- but if events work out as the museum expects, it will have some $50 million every year to spend on new construction and on works of art.

Meanwhile in nearby Pasadena, the Norton Simon Museum of Art is becoming one of the world's lovliest. As the Pasadena Art Museum, it specialized in showing contemporary art, but then Norton Simon, whose taste runs to Old Masters, lent to it his name, much cash and his collection -- and made the place his own. Simon does not seem to care much for new art. He recently sold off a large painting by Frank Stella, as well as many prints by Jasper Johns, Roy Lichtenstein, Moholy-Nagy and Pollock. He was going to sell pictures by Diebenkorn, Sam Francis, Agnes Martin and de Kooning -- until a lawsuit filed by three former trustees of the Pasadena institution stopped him in his tracks. Even those who think him selfish and short-sighted do not doubt that Simon's intentional retreat from contemporary art helped prepare Los Angeles for Hulten's new museum.

The new $16-million Museum of Contemporary Art will be built by the developers of the Bunker Hill project in downtown Los Angeles. Hulten plans to spend only one third of his time there until his contract with the Beauborg ends in September, 1981. Richard Koshalek, who now heads the Hudson River Museum, will move west to join him as deputy director/chief curator. The architect responsible for its $16 million building will be picked this month. Finalists include Kevin Roche, Romaldo Glurgola, the Englishman James Stirling, Arata Isozaki of Japan, Edward Larrabee Barnes and Richard Meier.

The Los Angeles County Museum of Art, thanks to $4.5 million from the Ahmanson Foundation and $2 million from Armand Hammer, is also growing. The museum's new director, Rusty Powell, who until last March was executive curator at the National Gallery of Art, says, "Starting early next year, we will expand our permanent collection galleries by 25,000 square feet. And that's just the start. Atlantic Richfield already has provided a $3 million matching grant for a yet-to-be-designed wing for 20th-century art."

The museum of Fine Arts, Dallas, will break ground this fall for a $45 million, 200,000-square-foot gallery addition designed by Edward Larrabee Barnes. A bond issue approved last November by the city's voters has generated $24.8 million in construction funds.

The Kimball Art Museum of Fort Worth, designed by Louis Kahn, also has a new director. He is Edmund P. Pillsbury, 37, the director, since its opening, of the Yale Center for British Art. (That New Haven art museum, given by Paul Mellon to his alma mater, was also, incidentally, designed by Louis Kahn.)

The High Museum, Atlanta, is also getting a new building. Designed by Richard Meier and partially paid for by Robert Woodruff, the $15 million building will approximately triple the Georgia institution's exhibition space. b

Though this regional progress is impressive, no one should suppose that a crop of little Louvres is now blooming in the desert. The museums there have cash, and remarkable new buildings. But what they lack is art.

"The combined collection of the Southwestern art museums," observes Harry Parker, who runs the one in Dallas, "does not equal that of, say, the National Gallery of Art."

And few on the East Coast are intimidated by the Sunbelt boom. "It is true that there is an electric feeling about Los Angeles right now," says Jane Livingston, associate director of the Corcoran Gallery of Art. "It is also true that everybody is inflamed about Pontus moving out there," adds Livingston, who worked in Los Angeles until 1975, "but hold on. His museum does not exist yet. Let's just wait and see."

"It's kind of interesting," says Livingston, "that all of this is going on outside the New York arena. Pontus comes from Paris. Koshalek was trained in Minnesota and in Texas. Pillsbury and Powell both worked with Paul Mellon outside of New York."

"The more you increase the number of museums, patrons and exhibits, the better it is for all of us," says J. Carter Brown, director of the National Gallery of Art. "The Sunbelt developments, it seems to me, do not hurt, but help Washington's museums. As rising fuel costs limit European travel, you're going to get more and more people checking out the galleries in the nation's capital. We're a little bit of everywhere. We're not against the museum decentralization -- we're part of it."