Saturday night a crowd of about 500 people crowded onto the steps in front of the Paris Opera. Some were waiting for the doors to open at 7:30; some were waving signs offering to buy tickets and others were there to watch the celebrities step out of taxis and limousines.

The event was the first presentation of the complete opera "Lulu," written by Viennese composer Alban Berg between the years 1928 and 1934. There is much more to "lulu" than meets the eye, however. Mysterious events surrounding the opera have given the world of music one of its most exciting detective stories of this century.

At the age of 50, as the result of an insect bite, the composer died, leaving what was believed to be the unfinished opera. The opera concerned itself with a woman who unwittingly wreaks havoc with the lives of those who know her.

Berg had signed a contract with the publishers, Universal Edition of Vienna, in 1930, and in the spring of 1934 announced that the work was all on paper and that he would get it orchestrated for the coming fall. It was just prior to this that the Nazis had come into power; as a "decadent" composer he was high on their hate-list. This meant jobs and income became scarce. He and his wife Helene needed income from whatever source was possible. He made an orchestral suite with excerpts from the new opera. A commission from the American violinist Louis Kramer was accepted.

Upon his death on Christmas Eve of 1935, the orchestration of the third act of "Lulu" was said to be unfinished. Shortly thereafter the widow was approached by her husband's former teacher, composer Arnold Schoenberg, then living in Hollywood, who offered to complete the work. The material was sent immediately but was almost as immediately returned, with the puzzling explanation that the job would be too time-consuming.

Alban Berg's position in the world of avant-garde music was such that the work, finished or not, was bound to be produced despite the Nazis. It was presented in Zurich with only Acts One and Two and with the two scenes from the suite which Berg had orchestrated. Until Saturday night it had been presented only in this two-act form.

This happened despite the fact that biographer Hans Redlich in the mid-'50s stated flat out that the work was virtually completed and could have easily been performed in its entirety in Zurich. At this point, it seems the widow Berg insisted that the biography also carry a statement saying the score had been shown to composers Anton Webern, Alexander Zemlinsky and Schoenberg (all, by this time, dead) and in their unanimous opinion, completion of the work was not feasible. Checkmate.

Move now to 1963, when publishers of Universal Editions decided to let American George Perle, a preeminent Berg scholar, come to Vienna to inspect the photocopies of the score. Perle repeated the Redlich statement -- that completion was not a problem -- and added that the concept of the work was not possible without the third act. (In the final act those destroyed by Lulu return, in a different guise, to destroy her.) Unanswered questions about what really was going on at the publishing house multiplied in number and intensity.

It was then that Frau Berg played a trump card: She professed to be in spiritual contact with her husband. It was his express wish, she said, that the third act remain incomplete and never be presented. She then set up a foundation to receive the copyright of the Berg estate and to execute the terms of her will. The will banned completion of the work; furthermore, the music was never to be seen by anyone.

That would have seemed to settle the matter for good. The publishers, however, having a signed contract with the composer from 1930 for a three-act opera, quietly had commissioned Viennese composer-conductor Friederich Cerha to complete the opera. After the death of Frau Berg, they quietly informed the foundation. Of course, the foundation had to take legal action and seek an injunction (apparently it was never granted).

On Friday Friederich Cerha held a press conference at the Centre Chaillot gallery in Paris to answer in minute detail as many of the unanswered questions as possible. The work had been virtually finished all the time, he said. The unanswered question was still: "Why the paranoia about the third act?"

The best answer is one pieced together by historians and biographers. It seems that Alban Berg was not the model husband that he seemed to be. Substantial evidence has been gathered to name another woman in his life. It also surfaces that Helene Berg felt that the last act of the opera reveals his double life and philosophy about it, and hence wanted the "secret," as she saw it, to go with her to the grave.

Seeing the third act for the first time Saturday night, I couldn't find a shred of such a confession.

At any rate, it has been the best and most durable item of kaffee-klatsch conversation for the avant-gardists of the last 40 years, and, for many of them, a crusade. Perhaps it will continue to be.

With the addition of the 64-minute third act the performance Saturday night ended at a little after midnight, and the 10-minute ovation was predictable. Ebullience and enthusiasm seemed unanimous.

Designers Richard Peduzzi (sets) and Jacques Smith (costumes) joined with Maestro Pierre Boulez and the full company to take serious, ceremonial and straight-faced (no smiles, no bows) curtain calls. Eventually the call-backs from the audience caused the company to relax to a more comfortable relationship with the public.

To successfully present this complicated, formalistic, cerebrally demanding work of the grotesque and shock era in the old-fashioned, opulent setting of the Paris Opera was no small feat.

Certainly it had much tender, loving care and an exceptionally large budget. Certainly it had an extra measure of in-house intensity focused on it because it was the dream of a lifetime come true for general director Rolf Liebermann.And surely the pressure of world attention must have been tremendous.

Teresa Stratas, the unmannered waif, the sex object, the tiger cat, the utterly sympathetic performer of the title role, made it a tour de force and a personal triumph. Perhaps this was the most significant performance of her illustrious but not fully appreciated career. She was consistent and beautiful and took top honors and applause from the audience.

Franz Mazura came in second in the audience sweepstakes. His Jack the Ripper was just right, but he was so brutal as Doctor Schoen that he lacked a human quality with which the audience could sympathize. His Doctor Schoen was the archtype of a Nazi storm trooper, utterly lacking in compassion. It was, nevertheless, a powerful and effective performance.

Pierre Boulez conducted the orchestra with a firm, knowing hand.

The settings by Richard Peduzzi represented the overwhelmingly ugly architecture of the period: green marble, gigantic stairs and a generally intimidating impression. Calculated to be so, certainly.

As for the device of the third act, using the victims as supposedly other characters for retribution, it didn't work. Possibly this was because so many of the victims were bullies in the first part of the opera; therefore there was no contrast when they became the bullies called for in the last act. Perhaps, too, it was a matter of same personality, whether it was first or last act.