Art and bureaucracy -- an improbable couple at best -- were formally married in Washington 20 years ago after a flirtation that dates back to the origins of the American republic.

Lyndon B. Johnson presided at the ceremony on Sept. 29, 1965, when he established the National Endowment for the Arts (NEA), with Roger Stevens as the first chairman and both houses of Congress as witnesses and sponsors.

It's too early to say that the odd couple lived happily ever after. There have been arguments, sometimes about money and sometimes about behavior. And neighbors, particularly on Capitol Hill, have complained more than once about the goings-on in this me'nage.

But 20th-anniversary celebrations (formally tagged National Arts Week) are popping up all over the map. There are 70 small-print pages of them in the NEA's not-quite-complete list of Arts Week events.

Anchorage is celebrating with an exhibit of works by native basket makers, Mobile and Richmond with jazz festivals, Spartanburg, S.C., with a performance of "Annie." A museum in Utica, N.Y., has an exhibit of "Disarming Images: Art for Nuclear Disarmament." Omaha has 14 events, including one called "Bagels and Bach With the Bluegrass Crusade."

In Washington, more than a dozen events are connected with National Arts Week -- at not only the museums and the Kennedy Center, but also the National Council on the Aging, which has an exhibit of "Cape Cod Visions," and the D.C. Commission on the Arts and Humanities, scene of Monday's Mayor's Arts Awards ceremony, which opened Arts Week here.

In a way, what these events are all celebrating seems quite simple: money.

But the marriage of art and bureaucracy is more complicated than that. Bureaucrats work hard at being colorless; artists tend to splash paint around, make loud noises or scribble obscenities. When their orbits intersect, you can expect curious results, such as this sentence from last year's NEA annual report: "The artist labor force grew by 47 percent in the '70's, with the proportion of women and minorities increasing substantially in relation to the overall artist population."

Artists prize their individuality. But they have accepted being abstracted into a "labor force" or "population," and even filling out forms (as many as 10 copies for the D.C. Commission on the Arts and Humanities) for the benefits of bureaucracy.

These benefits are not limited to cash grants, which have ranged from less than $1,000 to $1 million, depending on the recipient. There is also recognition; in the past 20 years, among ticket buyers and private contributors, National Endowment funding has become widely accepted as an arts equivalent of a high Department of Agriculture rating on a piece of beef.

In the distribution of money, the bureaucrats are a buffer between the artists and Congress, from which all blessings flow. Such a buffer is needed; artists and congressmen both tend to be prima donnas. They also tend to have rather incompatible attitudes and styles. What happens to the buffer, of course, is that it gets buffeted.

The latest episode, a few weeks ago, involved a trio of Texas congressmen who tried to have endowment funds withheld from artistic efforts found offensive to the average person. Their effort made a bit of noise and then was quietly buried by the endowment's congressional friends, who have by now accumulated a lot of experience in handling such problems.

In 1981 a group of senators tried to cut off NEA grants to individual artists (who tend to be unpredictable and cantankerous) and limit it to aiding institutions (which are generally better behaved). The movement died a quiet death, as do most congressional campaigns against the endowment.

But it has always offered handy targets. In 1977, for example, Sen. William Proxmire (R-Wis.) found a sitting duck among the endowment's thousands of beneficiaries. He gave one of his uncoveted Golden Fleece awards to an event in which artist Le Anne Wilchusky went up in an airplane, threw out colored streamers of crepe paper and filmed them as they drifted down to earth.

In the same year, Michael Straight, deputy and interim successor to the second chairman, Nancy Hanks, created a stir by resigning in protest against the "politicization" of the endowment. This was his description of the nomination of Livingston Biddle Jr., who became the third chairman. Biddle had been a special assistant to Sen. Claiborne Pell (D-R.I.), the chairman of a key subcommittee on arts and humanities and one of the chief authors of the law that established the endowment.

Pell, a strong supporter of the endowment, has been known to make life complicated for it. Frankly professing that "I don't like abstract art," he used to press the point in subcommittee hearings until the endowment finally invented, for his benefit, a series of categories defining the various levels of abstraction and realism receiving NEA support.

The National Endowment for the Humanities, founded simultaneously with NEA, makes headlines much less often. It deals with scholars, who tend to be less colorful (and perhaps more inured to the rituals of bureaucracy) than artists. But Humanities also cops an occasional Golden Fleece, it is paired with the Arts Endowment in charges of "elitism" that are shot off from time to time, and in 1975 it ran afoul of a labor union. After the Endowment for the Humanities awarded $250,000 to subsidize an American tour by England's Royal Shakespeare Company, it found itself denounced by an Actors Equity spokesman for "economic harm and insult inflicted on the American theater."

When it comes from potential recipients of grant money, that kind of charge boils down to a feeling that the money went into the wrong pockets. The same subtext can usually be read in charges of "elitism," such as in the 1980 letter 27 writers sent to Biddle accusing the NEA of "continuing instances of favoritism in the awarding of literature grants and fellowships."

Those charges struck directly at the NEA's "peer panel" system, under which applications from each field of art are reviewed and judged by consultative groups of people active in that field, and at its policy of choosing staff members who have been active in the fields they administer and are expected to return to those fields when their NEA terms expire. On the whole, these policies seem to have generated considerable respect for the NEA among American artists, who feel they are being evaluated not by bureaucrats but by fellow artists. But the closeness of NEA staff members to the arts they administer does make the NEA vulnerable to accusations by artists whose grant applications have been rejected. There are cliques and friendships in the arts, and questions of artistic merit often overlap with questions of personal taste.

The NEA tries to disarm such criticisms by dividing the responsibility for grant allocations among staff, which processes applications; the panels, which evaluate them; and Chairman Frank Hodsoll, who decides who gets what. The NEA's rules require staff or panel members to report all involvements that provoke suspicions of conflict of interest and to stay away from grant applications in which they might have personal involvement, pro or con.

Hodsoll is emphatic on one point: that NEA grants do not reflect his own tastes in the arts. "There are a lot of things we fund that I don't like," he says. Hodsoll, an attorney and a career civil servant, says his current appointment is "like any other government job, but the subject matter is more interesting."

In spite of public controversy and congressional snipers, he says, "of all the federal programs I've been involved with, this is the least subject to congressional district politics."

He believes the widespread respect for the peer review system is one reason for the relatively low pressure in his job. But he gives another reason that sounds more pragmatic: "Arts funding is not a survival issue like a road, a hospital or a sewage treatment plant."

Whenever a government spends money, there are taxpayers who think it is being misspent. Through the 1970s, while the NEA's annual budget was climbing toward and past the $100 million mark, there were sporadic, scattered protests (usually in Congress, sometimes in the press) about budget increases. In 1971, noting that the NEA's second chairman, Nancy Hanks, had boosted the budget from $2.5 million to almost $75 million in the endowment's first 10 years, columnist George Will called her "the Mayor Daley of the Arts." He also reported that Sen. Proxmire "has found the NEA budget as hard to cut as the Pentagon budget. When he attacked the soaring NEA budget, his phone rang off the hook with protests from grant recipients all over Wisconsin."

Proxmire's experience was not unique. In 1981 the Reagan administration ran into a similar flood of protests when it threatened to cut the Carter arts budget in half. Star-studded protest parades marched down Broadway to Lincoln Center; theaters staged momentary blackouts to dramatize the budget situation; volunteer lawyers began to talk about class-action suits of artists against the Reagan administration; audiences were given postcards to send to their congressmen. The arts appropriation did drop from $158.8 million in fiscal 1981 to $143.5 million the next year, but it didn't stay down for long.

How much tax money do Americans spend on the arts? The NEA appropriation for fiscal 1985 was $163.7 million, which comes to about 65 cents a person if the population is rounded off at 250 million. This compares with an original appropriation of 1 cent per capita in 1965. Estimates of total government spending on the arts (which presumably include military bands, as well as state and local subsidies) peg government spending at about $13 per capita. This makes the NEA budget look like what Hodsoll claims it is: "a small part of the arts picture." It is also a small fraction of comparable estimates made in recent years for Sweden ($35 per capita) and Canada ($32). But if private support (which is often tax-deductible here and is not a significant factor in many European countries) is factored in, Americans seem to be subsidizing the arts at a level of about $27 per capita -- approximately the same amount reported for government support in the Netherlands and West Germany.

It remains uncertain how these figures relate to a remarkable 1980 report by the Louis Harris polls, which said 51 percent of Americans claim they are willing to pay an extra $25 a year in federal taxes to support arts programs. For that matter, it remains unclear exactly what might be implied in that figure or whether anything should be done about it.

Beyond questions of money, accusations of obscenity, lapses of taste and alleged conflicts of interest, there are serious philosophical issues underlying the establishment of a National Endowment for the Arts. Should the government be involved in funding artistic enterprises? Aren't there dangers of establishing "official" styles and forms of art that would deaden creativity -- not to mention the possibilities of corruption when a high potentate's spouse, child or lover yearns for a career in opera or ballet?

The questions become more complicated in a democracy, where they spill over into the perennial issue of elitism versus populism in arts support. Hodsoll constantly faces problems unknown to his counterparts in the Soviet Union, where the arts (like everything else) are an instrument of government policy, or in most European countries, where government support of the arts is a long-established tradition.

In Europe, the royal houses toppled by various revolutions of the last two centuries usually had firm policies of supporting the arts -- sometimes because the potentates were lovers of the arts and sometimes because the arts contributed to their glory. When the thrones were knocked down, the new revolutionary government found that they had royal opera companies, orchestras and collections of paintings on their hands, and they took up the burden of support from their royal predecessors.

The American Revolution had no such heritage, and statements on the arts by the Founding Fathers tends to be enthusiastic but nonspecific. One of the best was made by John Adams in 1780 in one of his eloquent letters to his wife, Abigail: "I must study politics and war, that my sons may have the liberty to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture, in order to give their children a right to study painting, poetry, music, architecture . . . "

The first time the federal government committed itself to a long-range program of arts support (as opposed to commissioning a painting, for example) was the establishment of the Marine Band, our oldest musical organization, in 1790. Another giant step was the establishment of the Library of Congress in 1800. Then things quieted down until 1846, when the Smithsonian Institution was created. Plans for systematic federal encouragement of the arts were proposed in 1826 by artist John Trumbull, in 1859 by President James Buchanan, in 1879 by Rep. Samuel S. Cox (D-N.Y.) and by a congressional resolution in 1897. On all these occasions, many enthusiastic words were spoken but no money was appropriated. In 1909 Theodore Roosevelt actually appointed a 30-member Council of Fine Arts, but no money was appropriated and it soon disbanded.

The first systematic program of arts support was begun by the next Roosevelt, who launched such programs as the Federal Writers Project, the Federal Theater Project, the Federal Art Project and the Federal Music Project under the umbrella of the Works Progress Administration. But these were emergency measures to fight the Depression, and they withered with the return of prosperity. Proposals for a federal arts agency continued to pop up in Congress and disappear.

The final push, leading to the establishment of the NEA 10 years later, can be traced perhaps to the recommendation, in Dwight Eisenhower's second inaugural address, that "the federal government should do more to give official recognition to the importance of the arts and other cultural activities." If Ike was for it, who could be against it? Bills appeared in Congress with greater frequency, and in the Kennedy administration the movement finally came into focus with some clout behind it. It is possible (though not necessary) to view the establishment of the National Endowments as a part of the nation's final tribute to John Kennedy.

After 20 years, in spite of complaints and controversies, the NEA looks like a permanent and flourishing part of the American scene. Besides the $3.5 billion it has given to the arts (give or take $100 million), it has encouraged many times that amount in private giving -- an estimated $4.6 billion last year. And the results are apparent all over the American landscape, in orchestras, theaters, opera and dance companies, folk festivals and poetry magazines that would not exist without such encouragement. The current attitude of Middle America was perhaps best expressed around the Endowment's 10th anniversary in a newsletter to constituents by Rep. Lee R. Hamilton (D-Ind.):

"A nation which refuses to spend a penny for the arts for every $500 it spends on defense may find it has much less to defend . . . The arts are an economic as well as cultural resource. Money spent on the arts influences the economy of an entire community and has a multiplier effect. The arts are an asset to the tourist industry, they attract business and industry, and they enhance real estate value."

He might have added that sometimes they are even beautiful; but we all know that.