THE NEO-ROMANTICS, who invaded Washington in force last October, have now established a beachhead in New York, armed with melody and exotic sounds. A few members of the avant-garde, who are the new conservatives in music, tried to repel them with a barrage of boos, but they have dug in and are almost ready to proclaim victory. Music will be brighter and easier to enjoy once they have consolidated their strength.

The 1982-83 music season opened at the Kennedy Center with something like a manifesto--or perhaps a spontaneous demonstration. All the finalists in the Friedheim Awards (even the atonal "Avanti" by Gundaris Pone', which took the first prize) turned out to be prime examples of the new trend in music--a return to the warmer emotional climate of bygone times.

At Lincoln Center, the season is now ending with a similar demonstration. For the interval between its subscription season in Avery Fisher Hall and its summer season of concerts in the parks, the New York Philharmonic is presenting a festival of contemporary music, lectures and symposiums entitled "Horizons '83" and subtitled "A New Romanticism?"--with a well-chosen question mark.

The quizzical punctuation is justified by a lot of the music performed during the first week of the festival, which continues through next Wednesday. But so is the suggestion that we are returning to the ideals of the Age of Byron. The Philharmonic is presenting a mixed bag of styles and media that range from pointillism and minimalism to a computer-enhanced extravaganza by Morton Subotnick. But there is enough melody, emotional urgency and direct communication to show that something significant is happening to American composers in the 1980s. Their goals and methods are changing, and the change seems to parallel the beginnings of romanticism more than 150 years ago.

It is a sadder but wiser romanticism, perhaps--lacking some of the all-out, innocent impetuosity of the first time around--but it has the essential qualities. It is personal and intensely emotional; it wants to make audiences feel rather than analyze; it has a strong affinity for literary subjects and overtones rather than abstract structures; it is often tonal and uses melody where classicists would use motifs and serialists would use tone rows. It loves exotic flavors and big, splashy effects. And it goes for maximum impact without worrying too much about small details.

There were several outstanding examples in the first three concerts of the festival. On the opening night, the prime sample of romanticism was the New York premiere of "All in the Golden Afternoon," by David del Tredici. This score is a long, sometimes stormy evocation of the world of "Alice in Wonderland." It includes the Big Tune (reminiscent of "In a Monastery Garden") that keeps popping up in Del Tredici's "Alice" cycle--as the subject of a 100-page fugue, for example, in "Happy Voices," which was played in the Friedheim competition. But it is mostly descriptive music, with a power, a mastery of orchestral flavors and a lyric opulence comparable to Richard Strauss.

Romantic to the core was the New York premiere of John Harbison's Violin Concerto. It brought to mind the work of Tchaikovsky, Mendelssohn and Prokofiev--not because the composer consciously imitates these predecessors, but because he is interested in the same kind of values--virtuoso fireworks, intense drama, bright sound and personal expression. To judge by his program notes, Harbison is romantic not only in his style and structures but in the methods and circumstances of his composition. The concerto, he notes, "was written over a three-year period, but in very quick bursts (the opening tutti and thirty bars of the solo entrance were written one night in March, 1978, absolutely without premonition)."

Compare this to the usual descriptions of their work by contemporary composers--dry discussions of technical exercises in thematic manipulation--and you are likely to recall Coleridge talking about the mysterious origins of "Kubla Khan." The same qualities of mystery and headlong inspiration can be heard in the music.

In John Adams' wild and often comic "Grand Pianola Music," romanticism is seen being born out of the still-fashionable minimalist styles of Philip Glass and Steve Reich. It is scored for an orchestra of winds and percussion without strings, three sopranos in a wordless chorus and two pianos, which give the music much of its romantic flavor. The woodwinds open with a typical minimalist mantra--a tight little phrase repeated over and over and over and over, evolving gradually until the pianos and brass try to break in with a Tchaikovsky-style flourish. The work's three movements are a debate between the two styles, with the pianos wavering momentarily toward minimalism. But in the end (a rambunctious rondo), the pianos persuade the orchestra to join them in a mammoth climax with a tune that Rachmaninoff might have envied.

These were early highlights of a festival that could have had better focus. There were spells of dryness that served as a reminder of what the neo-romantics are rebelling against, and a lot of works in which not-particularly-romantic composers (Subotnick, Barbara Kolb, Toru Takemitsu) do their own interesting thing in their own way. At least one composer who is romantic but not neo, William Schuman, seemed to wonder why he was on the program. "I am an old romantic," he observed in a conversation in the lobby of Avery Fisher Hall. "It feels strange to be in the middle of all these new romantics." He does, in fact, represent a small but hardy band of composers (others are Alan Hovhaness, Ned Rorem and Elie Siegmeister) who continued to compose in an essentially romantic style during the lean years when serialism was the dominant trend. The others are unrepresented in the festival, as are a good many other American composers whose work might have added something romantic to the event.

George Walker, for example, and Ulysses Kay--eminent black composers whose romantic credentials are equal to any. The total omission of black composers, combined with what he sees as a consistent pattern of discrimination by the New York Philharmonic, led the music critic of the Amsterdam News, Raoul Abdul, to boycott the festival entirely. Women composers are also underrepresented (Barbara Kolb is the only one in the festival), but thematically the problem is the omission of many composers who are romantic and the inclusion of quite a few who are not.

Some critics have suggested that the use of "Romanticism" in the festival's title was a marketing device. If so, it worked--in combination with a low price for series tickets. The Philharmonic is packing its hall nearly to capacity for programs of contemporary music--a genre that a few years ago would play to audiences numbering in the dozens. The size and enthusiasm of the audience, in fact, was as sure a sign as any that neo-romanticism has arrived. If audiences come, can composers be far behind?