SAFE HOUSES. By Lynne Alexander. Atheneum. 262 pp. $13.95.

THERE IS nothing safe about this audacious first novel of Lynne Alexander's. The characters are in constant danger of madness or despair; the author takes real risks at every turning; and the reader is given no quarter in a chimerical world where disaster is comical, good news is dangerous, and the basic facts are simply unattainable.

The premise of the story is based on monumental historical license -- the Doctorow ploy taken to new limits: Gerda, a Jewish beauty of 18 in wartime Budapest, is living at the Majestic Hotel where her father is maitre d'hotel. He has successfully obscured his family's Jewishness and is selling his daughter's favors to the powerful men in and around the hotel as a form of insurance. Adolf Eichmann moves into the Majestic and uses it as headquarters for the deportation of Hungary's Jews; inevitably, Gerda is recruited to service his sexual needs.

At the same time Raoul Wallenberg comes to Budapest and begins his drive to save the city's Jews from destruction, and Gerda becomes his mistress and his conspirator, tipping him off about Eichmann's plans. When the city falls to the Russians, Wallenberg naively puts himself in their hands and is immediately imprisoned. Gerda, to save herself, tells the Russians that Wallenberg has been working with the Americans, thereby sealing his fate. When she leaves Budapest she is pregnant. Whose child is it, Eichmann's or Wallenberg's? Gerda doesn't know, she says, but she tells the child (Rella, a girl named for Raoul) that she is Wallenberg's. They are living in Brooklyn Heights and, in the years between 1956 and 1981, Rella's life revolves around the myths of her father's death or survival in Russia. Gerda couldn't care less -- what's over is over, and good luck to him -- but Rella is obsessed with the idea of Wallenberg's safe release. Sharing her obsession is a fellow named Jack Baum, who lives on the top floor of their apartment building and who in 1945 was pastry chef to Eichmann at the Majestic.

All very improbable, and Alexander adds to the improbability, keeping us constantly off balance. The middle-aged Gerda has little regard for the truth ("What is truth, anyway? One leads a rich and varied life, naturally the memory isn't always crystal clear. One makes a choice. One tells -- What else? -- the best story"), and we begin to realize that she may never have been Wallenberg's lover after all. Rella's quest may be pathetically beside the point. But the story itself hinges on the premise of Gerda's two lovers, Eichmann and Wallenberg, so that reading it, one is left with the deep uneasiness engendered by a house of mirrors.

BEYOND THAT, Alexander has taken great chances with the three main characters. It's tricky to center a book on an unsympathetic character without turning readers off, and Gerda is no sweetheart. She lives immured in her ground-floor apartment, where she makes a living by prostitution and later by involvement in a heroin deal, and where she observes her child's development with distaste: "Her nostrils are trimmed with the color of trichinosis pork . . . She is like a happy sardine, flipping around with those silvery grey teeth; it is quite painful to witness." Rella's anorexia and lack of self-care are repugnant to Gerda; she finds her daughter's despair contemptible and her happiness equally repellent.

And yet one enjoys Gerda. Her self-satisfaction is so complete that it makes a kind of zany sense when no one measures up to her own standard, in her eyes -- and her cynicism is so pervasive that one doesn't expect her to reach out to anyone else; what would be the point? She isn't really malicious; she even does the odd good turn if it doesn't involve real effort. And her sardonic tale of life is funny, even compelling.

Jack, on the other hand, is pathologically good. Another risk: it's hard to write about goodness without coming up with treacle. What Alexander does with Jack Baum is to make him ridiculous -- silly -- and deeply good. It works. Jack is a mad baker. He speaks lasciviously of pastries and refers to women as baked confections. In fact he sees all people as desserts. His great moment of valor comes at the Majestic when, having been ordered by Eichmann to make a cake for a dinner with Wallenberg in the shape of a shiny, dark swastika, he creates instead a towering white mountain of cake and spun sugar, an acton of such trembling brave intensity that we laugh and quake at once. His contribution to the Resistance is in pastries, but it is his all. Flickering in and out of madness and buffoonery, he is a masterful creation. We come to feel that by sheer commitment he is going to keep everyone safe -- Gerda, Rella, Wallenberg, and even us, the readers.

That is an illusion. "There is no safety except in death," reads the message that Alexander is flashing to us with her box of tilted mirrors. Everyone in the book is looking for safety, but freedom and safety are mutually exclusive.

This is an intriguing piece of work that, even when it misses, misses with distinction. The character of Rella, unidimensional in her pathetic obsession, is pitilessly used as symbol and never attains believability. Her final fate is so symbolic as to leave the reader feeling had. Then, too, if all the suspense in the book lies in Wallenberg's fate -- which of course remains unknown -- in the end, the story line falls flat and the symbolic system is left to carry the day alone. But the book has power and charm. Our affections are engaged, against all the odds; Jack and Gerda, lunatic baker and whipped-cream odalisque, pull us through the crazy house and make us like it.