This much, and little else, may be said with certainty about the 35th Biennial Exhibition of Contemporary American Painting which opens Saturday at the Corcoran Gallery of Art: The stress is on abstraction. There are 24 painters in it, some of whom are old, some of whom are young, none of whom is famous. It is a handsome, useful show.

It demonstrates convincingly that in a dozen regions of this country, not just in the art centers, serious abstract painting is alive and well.

The painting of the '70s is not the painting of the '60s, though the differences are subtle. One senses at the Corcoran show a decrease in wild flailing, a patient reassesement of the lessons of the past, a deepening concern with surface, with how paint is put to canvas. This is not a shocking show. It is not the New that rules here, it is rather the mature.

Though viewers tend to draw generalities from group shows, few arise from this one. It is not one exhibition, it is 24.

Some of them I loved, some made me grit my teeth. Seen together here these two dozen shows allow one to re-test already formed opinions. One experiences again the beauties of the patient, the subtle and the fine, and the pitfalls of the "Me Me Me" of messy, self-indulgent clutter. The 35th Biennial teaches the beholder as much about himself as it does about the state of contemporary art.

Corcoran curator Jane Livingston and Roy Slade, the director, who together picked this show, have given us good gifts. They have displayed for the first time, the paintings of Ray Herdegen of Minneapolis, Martin Myers of Berkeley, Frederick Hammersley of Albuquerque, Max Cole of Pasadena, Herbert Creecy of Atlanta and Houston's John Alexander. There are other gifted artists here, but the works of these six are enough to justify a visit.

Seen from across the room, the canvases of Herdegen have the inoffensive quiet of old rain-washed walls. But their surfaces are awesome. The startled viewer, who peers closely at these paintings, feels he has been given the viewpoint of an astronaut, a giant or a god.

A painting by Herdegen is not just one stained canvas. Rather it's assembled of, say, 200,000 miniatures - tiny colored dots that form a kind of map of pathways, forests, settlements. His works seem as large as continents.

The skyscraper puns of Myers are the wittiest works on view. Part painting and part sculpture, part color-grid and part toy, they allow us for the first time to feel some affection for the glass-sheathed towers that blight most U.S. cities.

New Mexico's Hammersley, who was born in 1919, achieves much that is profound from the most austere of means. Like John McLaughlin, the late California master, he assembles from the simplest shapes - squares, rectangles and arcs - works that grow and grow.

Cole's paintings, too, have precedents. Behind them one perceives the lessons taught by the grids of Agnes Martin. But Cole's work is not derivative. It is as finely detailed as Herdegen's. It is highly peaceful. It has presence and integrity. Her paintings seem to glow.

Alexander's abstractions suggest an overwhelming sense of specific place. They seem to be portraits of some shallow stream rushing over pebbles, through woods. Abstraction and representation are often held to be mutually exclusive, but in the riverscapes of Alexander, as in Myers' sky-reflecting towers and the hard-edge windows here by Michael Clark, abstraction and the representational coexist and do not clash.

There are other pictures here of interest - the subtle polymer and fibermesh paintings of Gregg Renfrow, the strongly tiled fields of Washington's Alma Thomas (who is in her 80s and still growing), the large heraldic forms of Michael Goldberg ( who used to be described as a "2d generation abstract expressionist") and "Glider," a huge and powerful picture by Paul Brown.

I also admired the finely crafted wall-sculptures of Tony DeLap, and the paintings of Paul Dillon which, though composed of Blondie comic strips applied to phonebook pages, manage to appear formal, stately, grand.

"The Life of Red Eye the Rooster," a cycle of 40 story-telling drawings by O. W. "Pappy" Kitchens, a Mississippi folk artist now well into his 70s, seen somehow out of place here, charming as they are.

I find little charming in the thick and cracking paint that weighs the surfaces of Darryl Hughto's pictures. Lucinda Parker also encrusts canvas, though while Hughto's colors are pretty, hers seem intentionally garish. I had just about decided that the newer works of Larry Poons and Jules Olitski had misled the young, but then I was seduced by the lovely colors used by Sandi Stone, yet another fan of impastoed paint. She's good.

Curator Jane Livingston is a fan of Virginia's David Headley; she has show his work before, but Headley's cluttered pictures, with their references to Morris Louis, Helen Frankenthaler and many other painters, fails. They look as if they were made not by one man but by 10. Headley throws in little cartoons, what seems to be Morse code and a scribbled shopping list ("yoghurt, milk, donuts, wine, pepper"), everything in fact but the kitchen sink.

A $60,000 grant from the Cafritz Foundation of Washington, and $20,000 from the National Endowment for the Arts, paid for this exhibition and its illustrated catalog. (Livingston writes with accuracy and insight; her essay is first-rate.) The 35th Biennial closes April 10.