WHEN ANCIENT Greeks wanted their great public buildings and plazas adorned with art, they went out and got their best artists to do the job - Phidias and Praxiteles.

When the Renaissance princes and popes wanted to decorate great public spaces like St. Peter's in Rome, they got the best - Michelangelo, Raphael and Bernini.

And when the U.S. government wants to decorate a new federal office building here or in New Orleans or Seattle or Honolulu or Fairbanks, who do they get to adorn those endless walls and yawning plazas? To cynics, the answer may come as something of a shock.

Over the past four years, the proliferation of first-rate public adornments in America - works by Calder, Nevelson, Oldenburg, Baskin, Stella, Bolotowsky and others - has been nothing short of astounding. And now, as in the past, much of its is connected to the construction of new public buildings - courthouses, federal offices and the like. The surprise is that the biggest single patron of public art today is none other than the General Services Administration, GSA, the nation's largest builder and landlord, and the government agency that oversees the design and construction of all new federal buildings. After the head of the National Endowment for the Arts, the head of GSA is potentially the most important patron of the visual arts in America.

This became clear in the early "70s, when Congress hurriedly authorized 60 new federal buildings. In 1972, under the leadership of GSA Administration Arthur F. Sampson, and with a push from the Arts Endowment's Nancy Hanks, GSA revived a nearly defunct "Art in Architecture" that had been established under Kennedy a decade earlier. It stipulated that one-half of 1 per cent of estimated construction costs was to be used to commission contemporary American art for new federal buildings.

Unfortunately, Sampson's successor, Jack M. Eckerd, recently reduced that amount to three-eights of 1 per cent. Eckerd resigned in mid-February after being asked to stay on by the Carter administration in a move designed to help to depoliticize GSA. No successor has yet been appointed.

Though even one-half of 1 per cent was less than the alloted for the purpose by Canada, where 2 per cent is the rule, or in western European countries, which range from 1 to 2 per cent - including Luxemburg - it was a giant step for the U.S., which hadn't been deeply involved in art patronage since the WPA.

Since 1975, as a result of GSA's newly revitalized "Art in Architecture" program, art has been going up adjacent to new government buildings everywhere, dozens of major sculptures along with murals, tapestries and fiberworks, all by first-rank American artists. GSA kicked off what has become a "golden age" of American sculpture by spending $311,000 on four projects in fiscal '74, including the great Calder "Flamingo" in Chicago. By the next year the figure jumped to nearly $2 million for 31 works connected with 20 buildings.

Suddenly there was an Isamu Noguchi in Seattle, a Louise Nevelson in Philadelphia Baskin in Nashville and Duayne Hatchett in Rochester, N.Y. There was a Robert Maki in Eugene, Ore., Jack Youngerman and Dimitri Hadzi Portland, Ore., Frank Stella in Wilmington, Del., and a sculpture by George Rickery in Honolulu. All of the above for less than the cost of a Jackson Pollock painting at current prices.

The reverberations of that injection of funds are still being felt. Come spring, Claes Oldenburg's "Bat Column" will go up in Chicago, as will Al Held's murals in Philadelphia. Also being readied is George Sugarman's "People Sculpture" in Baltimore, whic GSA courageously decided to go ahead and build, despite shrieks of horror from a group of Baltimore judges who, by their impassioned opposition, made themselves the subject of cartoons recalling Dumier at his best.

And next Friday night, Washington will get its first look at the most recently completed GSA-funded project for the new Labor Department Building: four murals - measuring 12 feet square by Jack Beal, a Richmond-born, new-wave figurative artist - outlining the history of labor in America from the 17th to the 20th century.

"I have never worked on anything so all-consuming," said Beal in the New York loft where he completed the huge paintings before rolling them up and bringing them to Washington last week for installation. "The government has given me an opportunity to do the most important project of my life, and has given staunch support and no interference whatever. If you're going to have art patrons, that's the kind to have."

As for the results, critics, after previewing the works in New York, were uniformly surprised and enthusiastic over the marriage of an old idea - story-telling murals - with avant-garde realism.

Around the other side of the Labor Department building is the other recently commissioned GSA gift to Washington, Tony Smith's monumental steel sculpture which, from some vantage points, looks like the abstract equivalent of the traditionally portrayed arm of the worker, fist clenched and sleeve rolled up, making a mighty muscle at the sky. The work was placed without fanfare last fall because it has yet to be painted sky blue.

The day-to-day management of this program is handled from a peppy little 5th floor office with orange doors at GSA headquarters here, where able and unflappable former architect Donald W. Thalacker has been building and polishing the "Art in Architecture" program since 1973 when it was revitalized by Sampson. His staff has just expanded to three.

Thalacker's first task, at Sampson's request, was to set up sensible selection procedures and guidelines, which he did with the help of Brian O'Doherty, then head of Visual Arts at NEA.

Previously, works had simply been selected by the architects. Now architects are informed that they can incorporate art into their original design concept, and if they choose to do so, the National Endowment for the Arts is asked to appoint a nominating panel of qualified art experts to meet with the architect at the site, and submit the names of three to five artists they consider most qualified to carry out the commission. The names are then submitted to an in-house GSA design Review Panel, with the administrator of GSA ultimately responsible for the final decision.

Although the system has produced a lot of good art, it has also, inevitably, produced controversy such as the Baltimore-Sugarman flap, which confronted Jack Eckerd when he took over GSA in November, 1975. Nicholas Panuzio, Commisioner of GSA's Public Buildings Service, which directly oversees "Art in Architecture," explains that for that reason, contract awards for new art projects were temporarily suspended until the program could be examined and the procedures revised to avoid as much future trouble as possible.

In the meantime, the amount of money spent on art dropped nearly 90 per cent in fiscal '76 to $232,000, though $604,000 was earmarked. And as of January, 1977, only two GSA buildings had been allowed to contract for art in fiscal '77. One is the South Portal Building of HEW here, which will get a James Rosati sculpture and a Breuer tapestry. twenty more buildings are backlogged and waiting for art.

Eckerd's long-awaited revised procedures were finally signed just before his resignation in mid-February, and in addition to calling for the cut from one-half to three-eights of 1 per cent, they insist upon the inclusion of art laymen (along with experts), on future nominating panels "to broaden community involvement and support." Though details have not been released, the art world is fearful that potentially controversial art may thereby be cut off along with the controversy. In any case, with Eckerd's departure, his new procedures become less important, because the next GSA administrator can simply change them, no doubt after another prolonged study and overhaul.

The entire program, in fact, depends on the whim of the GSA administrator and the commissioner of the Public Buildings Service, both political appointees who may or may not care about art, and who are likely to chage at least as often as the administration.

It is they who currently decide what kind of public monuments - buildings as well as sculpture - our civilization will leave behind to stand alongside those of Praxiteles, Michelangelo and Bernini.