It was the company of companies in the ballet of ballets. If the overflow crowd at Wolf Trap Monday night went more than slightly hysterical in reacting to the Kirov Ballet's opening night "Swan Lake," it was perfectly understandable.

It's not a question of the Kirov's being the "greatest" ballet company on earth, though by anyone's accounting it's assuredly a front-runner. It's that the Leningrad-based Kirov is unique in its heritage -- the company that produced Pavlova, Nijinsky, Balanchine, Fokine, Ulanova, Nureyev, Makarova and Baryshnikov, among so many other immortals, and the same company that gave birth to "Sleeping Beauty," "The Nutcracker" and, yes, "Swan Lake" itself.

The Kirov does not claim to be the oldest existing ballet troupe in the world. The company's own publicity material acknowledges the Paris Opera Ballet (also soon to visit this country and Washington after a long absence) to own that honor. But classical ballet in the form known to contemporary culture owes more to the Kirov (and its predecessor companies of the 19th century, in St. Petersburg's Maryinsky Theater) than to any other single source. It's the mother lode of ballet, the fountainhead, the true cross, or as close to it as modern times can come.

The company's four-night Washington appearance, as the last stop in the United States on a tour that started last month in Vancouver and ends in Canada June 14, has special symbolic significance. Before the curtain rose, the audience Monday night heard a recorded message from President Reagan, welcoming the Kirov as the first major performing arts attraction to reach these shores as the result of last year's summit meeting in Geneva. The message will be part of a national telecast next Saturday, to be based on tapings made Monday night and last night at Wolf Trap.

The Kirov hasn't visited the United States in 22 years, and the company seen Monday night has a new artistic director (48-year-old Oleg Vinogradov, who's held the post since 1977), a new cadre of principals, and virtually an entirely new ensemble. Yet the impact of seeing the Kirov today is as devastating in its way as it was in 1964, on its last visit, and for mostly similar reasons.

In short, the company is awesome, in its perfection of style, its technical power and assurance, its unanimity of spirit, and in the majestic scale of it all. The corps de ballet alone, in its precision of alignment, its easy command of technique, its innate stylistic authority, is a breathtaking spectacle.

If one must qualify one's admiration, it is only to note that the whole of the Kirov -- today as in 1964, though not necessarily in between -- is conspicuously greater than its parts. That is to say, the totality of the company as witnessed in Monday night's "Swan Lake" -- the dancers and the dancing, the staging, decor and musical interpretation -- was more impressive in its entirety than any single contributing element, and in particular, more so than any individual artist.

The paradox of the Kirov is this: One can see in its grandeur and refinement of form the very basis of the artistic excellence of the troupe's luminaries of past generations -- from Nijinsky to Baryshnikov, for example. But one can also see -- in the company's tradition-bound aspects, in its uniformity of approach, in its 19th-century sensibilities, in the very perfection of its morphology -- why those who left it to explore other horizons did so.

For all its uniqueness and indisputable class, there's a certain remoteness and anachronistic isolation about the Kirov. It's like a museum piece so rare and precious and ancient that one wouldn't dream of touching it. It's true enough that the Kirov has undergone modernizations and remoldings of many kinds since the days when Marius Petipa was at its head. Yet it retains to this day a sacrosanct aura that ultimately cannot be, and perhaps shouldn't be, "updated" for the sake of contemporaneity. This would mean the loss of its priceless identity. At the same time, the rigor of its foundations implies a degree of stasis, of conformity, of rigidity of convention.

The tradition upon which the Kirov rests was actually forged from a fusion of many national strands of ballet, especially the historic contributions of France and Italy. But the troupe is unmistakably Russian in character, and this was evident Monday night even before the dancing began, in the way conductor Evegeny Kolobov led the Filene Center Orchestra in the "Swan Lake" Overture. The opening oboe solo, with its announcement of the ballet's fateful and melancholy theme, was distinctively Russian in its languid tempo, its mournful cast, its italicized romanticism. And the rest of the Overture followed suit. The orchestra played with uncommon suavity, and an intensity of utterance seldom heard in domestic accounts of the score. Throughout the evening, the familiar Tchaikovsky music took on a fresh glow and accent, from an interpretive standpoint -- a markedly Slavic hue that one cannot imagine a western musical director achieving even by conscious imitation.

No less distinctive was the Kirov's staging of the ballet, attributed in the program to Constantin Sergeev, the company's director on its previous U.S. visits. There's the bravura role of the Jester -- a Soviet touch in this and other Russian productions. There's a Von Rothbart who actually dances, as well as grimaces menacingly. There are choreographic and musical features of many sorts different from what we are used to from western versions, even though all of these have their roots in the St. Petersburg soil.

On the whole, Monday night's "Swan Lake" was more admirable as an integrated conception than as a touching myth or interpersonal drama.

In any case, Galina Mezentseva seemed an eccentrically mannered Odette-Odile Monday night, showing off the fabulous flexibility and amplitude of phrasing that derive from Kirov training, but never getting more than skin-deep into the dual role of the heroine. Her Odette was on the aloof, almost spectral side; as the duplicitous Odile, she took on an aptly hard-edged veneer -- almost like a Soviet Joan Collins -- without, however, being fully on top of the technical challenges involved. Evgeny Neff, her Siegfried, looked like a well-schooled partner, but his own solo dancing was less than prepossessing. Vitaly Tsvetkov made a flashy, high-flying Jester, but he wasn't a consistently meticulous technician. Perhaps the most outstanding dancing came in the first act Pas de Trois, and especially from Irina Tchistyakova and Aleksander Lunev, who displayed qualities more akin to those we know from Kirov dancers now in the West than anyone else in Monday night's cast. Above all there was the corps de ballet, and the ensemble work in general, which fully matched the classical ideal the name "Kirov" has come to signify the world over.