AFTER TWO DECADES of steady growth, Washington is entering a new stage in its cultural development -- and earning a new reputation both in New York and around the country.

Following a long period broken only by the contributions of such wealthy patrons as Andrew Mellon,Elizabeth Sprague Coolidge and Gertrude Clarke Whittall -- contributions that were more national than local in focus -- the capital began to join in the arts expansion developing around the country in the '60s. One after another, new museums opened -- the National Portrait Gallery, the National Collection of Fine Arts in the '60s, the Hirshhorn and the East Building in the '70s. In 1971 the Kennedy Center started its first season.

Though Washington was turning itself into a glittering showplace for the arts, the general view was that the city was doing little in the way of developing its own voice. Apart from the Washington color painters and such isolated efforts as several Arena productions that went to Broadway -- "Great White Hope" in 1968, "Moonchildren" in 1972 -- and the National Symphony's Sunday afternoon New York series, the rest of the country heard little from the city's artists.

Then in the '70s a series of new groups joined the scene -- the Folger Theater, the Floger Consort, Contemporary Music Forum, New Playwrights and 20th Century Consort, to name only a few. Washington was, indeed, reaching toward a further cultural maturity.

Finally, within the last couple of years, Washington artist have aggressively moved out to the New York and national scene, prompted in large part by economics. The lack of a large corporate community and limited availability of either city or federal funding have forced groups to seek opportunities outside the city if they want to continue their artistic growth.

"There's been a period of proliferation of groups, and they're all reaching a level of maturity at the same time," said Christopher Kendall of the Folger Consort. The increased credibility of the Washington cultural scene, he added, "has gone hand in hand with the groups as they grown and develop. They serve both as an indicator and a cause in the city's developing reputation."

At the same time that Washington groups are reaching out, outside groups are clamoring to perform here. Jim Murtha of Gurtman and Murtha, a New York firm of press representatives whose clients have included Claudio Arrau and Vladimir Horowitz, spoke of the Kennedy center as "looming over the cultural life in America. It's mentioned all the time since the president goes and there are national telecasts."

"Carnegie Hall used to be the international house," added Murtha. "That kind of acceptance has come to the Kennedy Center within the last few years."

"Washington was always an important tour city," said Patrick Hayes, managing director of the Washington Performing Arts Society. "Now it is an absolute must."

For its current tour, the Los Angeles Chamber Ensemble, which played at the Kennedy Center recently, insisted on having a particularly strong soloist -- Russian emigre pianist Bella Davidovich -- in only two places -- Carnegie Hall and the Kennedy Center. The ensemble is using other soloists everywhere else.

"We would probably not bring major artist from abroad without booking them into Washington," said Harold Shaw, who directs a large artists-mangagement firm in New York. "It can be a problem when there are four or five groups wanting to go to Washington on the same day. In the past there was a way of throwing up one's hands and saying, 'Well, there's only Lisner and it's already booked' -- you can't do that anymore."

"I've seen Washington change from being a dismal city to take anything that had quality to being a marvelous, marvelous place to play," said New York producer Robert Whitehead, who has brought such productions as "A Texas Trilogy" and "No Man's Land" to the Kennedy Center. "I toured a lot in the '50s and '60s," he said. "At the idea of doing two weeks there your heart sank. Nowadays it's generally five weeks. There's only really three cities -- Toronto, Washington and Los Angeles -- when you can stay that long with some kind of security. These are the three most significant bookings in the country by far [outside New York]."

All three cities moved into this position during the past decade primarily as the result of a new building or, in the case of Toronto, an old building newly renovated.

"The Kennedy Center focused on the arts in such a big way and spectacular way that it galvanized the public into paying attention to the arts in a very special way," said Whitehead. "The audience has changed as well," he added. "Their priorities are tougher than they were 10 years ago. In the beginning taste was secondary to the occasion. The occasion -- that is, the play -- is now the thing."

Many feel that benefits from the Kennedy Center have spilled over to local performers. "People tend to identify a city in terms of what cultural institutions exist," explained Alan Marks, a New York musician and former director of a contemporary music series at the 92nd Street "Y." "The fact that a lot of New York groups have been playing there [at the Kennedy Center] and National Public Radio has broadcast from there gives a lot more credibility to the scene and so musicians coming from the city are apt to be viewed with more interest."

"There was no question but that we were viewed as a group of national interest," said Dina Kosten of the Theater Chamber Players, referring to the ensemble's tours around the country. "In most of the places we played newspapers talked about the group as the Kennedy Center's resident ensemble."

The Kennedy Center is, of course, not the only Washington institution that lends its luster to performers. The New York Times review of the Floger Consort's recent debut in New York began with a reference to the "distinguished scholarly institution" that houses the ensemble, the Floger Shakespeare Library.

In considering the possibility of taking on the Consort as clients, Gutman and Murtha also took note of the institutional connection. "The fact that the Flogr Library would put the group in residence was one sign of arrival, of professionalism in itself," said Murtha.

Buoyed by the growing cultural prominence of their capital as well as their own maturation, Washington groups are now approaching New York with a more confident attitude.

Under the Smithsonian umbrella, the Smithsonian Jazz Repertory Ensemble, The Smithsonian Chamber Players and the 20th Century Consort have joined forces this season to present a New York series, which marks the debut there of each ensemble. "We don't feel particularly humble about going to the big city," said James Morris, director of performing arts at the Smithsonian. "One does go play in New York at a certain period, but we didn't go with hat in hand saying, 'Aw, shucks, I hope they like us.'

"Years ago Washington was not a music-making center," added Morris. "You had to validate your chit out of town. That's no longer true. We were coming to New York as already-established performance groups with successful recordings. We wanted to play for the New York audience, but we were not dependent upon it for our livelihood."

Critical acceptance in New York is, and probably always will be, crucial in generating wider touring opportinities and, in the case of music groups, recording possibilities as well. What is of interest, as far as Washington is concerned, is the constellation of groups from the city currently active on the New York and, in several cases, the national scene.

The Folger Consort made its debut in New York last month. In January, the Theater Chamber Players, with a New York debut and a Carnegie Hall debut (this past December) behind them, opened the first of a three-concert series at the 92nd Street "Y." It is significant to note that the series was scheduled at the request of the "Y." In the fall, the Contemporary Music Forum will enter the New York scene with a concert at Symphonyl Space.

The Washingtn Ballet is scheduled to make its New York area debut this fall at the Brooklyn Center for the Performing Arts. And New Playwrights' Theater, established eight years ago for the development of original plays, will not have more of its plays produced around the country, including two in New York, than were done during the entire previous five-year period.

Three months ago, three plays associated with Arena Stage were running on Broadway. Two of them. "The 1940s Radio Hour" and "Loose Ends," originated at Arena and the third, "Teibele and Her Demon," received further development after originating at the Guthrie Theater in Minneapolis.

The Floger Theater is actively trying to send more of its shows around the country and currently plans to tour its production of "Macbeth" as far west as Kalamazoo and Kansas City. The Theater Chamber Players already has made two national tours and plans a third next year. All of the groups associasted with the Smithsonian New York series plan to tour next year.

With this fluorescence of activity, many observers would like to see Washington assume a special role within the nation that more nearly resembles that of other political captials.

"The biggest question facing Washington is what image does its cultural leaders want for the nation's capital and can they afford it under the current system," said New York artist-management director, Harold Shaw.

"Washington, D.C., has to receive funds from the federal government, whereas the New York Philharmonic and Buffalo and Rochester can get substantial chunks of the state budget as well as NEA funds," Shaw said."Is the nation's capital going to be shortchanged imagewise because it doesn't have the privileges granted to some of the other states?

"I think Congress in general underestimates how every private citizen feels about the nation's capital and how proud he is of it. Congressmen have to consider not just what they want to do after they go home at night, but what people across the country want their nation's capital to have," added Shaw. "If you scratch someone really deeply in this country, I believe he would say that if we're going to have museums and orchestras and ballet companies at all, the best ought to be in our nation's capital."

Few dispute that New York, given its population size, will remain the nation's standard-bearer. Instead of aspiring to that burden, Washington may well find its fulfillment in winning the country's heart.