Not long before he abandons his family forever, King Connors, the father in Alice Hoffman's fourth novel, "White Horses," gives his daughter, Teresa, the following advice: "Don't ever bother with the past. I mean it. . . . Who wants to be reminded of everything you don't have any more?"

In this novel, the past is a beautiful but ominous place, where men called "Arias"--legendary outlaws of the New Mexico mesas--ride out of a grandfather's yearning and into the imaginations of a daughter and a granddaughter, making what might have been an ordinary, unhappy California family into a doomed one, tormented by incestuous love and impossible dreams. "White Horses" is the lyrical and moving account of rude, aggressive men who are going nowhere, and of passive, dreaming women who deserve better than they have but who cannot find a way to live until they learn to live with a different kind of dream.

Twenty years before the novel opens, Dina, Teresa's mother, has eloped with King Connors, believing him to be like the "Arias" of her father's stories. "They don't think about right and wrong the way we do," her father has warned her, "they never care about yellow roses along a stone wall or dinner served on a china plate or someone to talk to. Any man who tells you he wouldn't give his skin to be one of them is a liar. . . . But a woman who goes looking for them deserves every damn thing she gets, and what she'll get is loneliness, day and night."

Although King Connors gives Dina plenty of loneliness, he is an ordinary mortal who works on a construction crew, drives a pickup truck and has a fierce temper. He leaves the family early in the novel. The oldest son, Reuben, soon follows King, leaving Dina to get by as best she can with the other son, Silver, and 13-year-old Teresa, the novel's protagonist.

Dina, though nearly 40, is still the child of 10 who wishes to be rescued. After King and Reuben leave, she gives up housecleaning (some readers may find in this novel a feminist fable for our times), allows her garden to go to weeds and awaits salvation, all the while nurturing young Teresa on tales of handsome men who thunder across the land at night.

Recoiling from the unhappiness of her family even before King Connors leaves, and suffering from bouts of a sleeping disease which no doctor can diagnose or cure, Teresa turns to her brother Silver for love and help. "Silver would have protected them all," she thinks. Years later, when she is trying to make a life with another man, she dreams of Silver as a man who "rode through a tundra bordered by rocks so strange they might have dropped to earth from Saturn. In her dreams Silver called her name, he was circled by a ring of fire, consumed by flames."

The real Silver, whom Teresa and Dina perceive as the "Aria" in the family, is no fiery hero. The real Silver is a self-absorbed, mean-spirited boy who drops out of high school, becomes a small-time holdup man and then a big-time drug dealer. The real Silver sleeps with countless women (he is so handsome that even strangers press their phone numbers on him) and is indifferent to all of them, though he finally marries Lee, the one who gets pregnant. The real Silver is the archetypal cad and fool, made appealing only by a ludicrous ideal of manhood.

The novel does offer an alternative ideal in the person of Bergen, the detective who was hired to find Dina after she eloped wth King Connors but who does not really enter her life until she has been abandoned. Bergen is a man who likes families, dogs and flowers. He is an earthy man, not a night rider, who begins his courtship of Dina by bringing a hundred-pound sack of compost for her garden.

"White Horses" is an ambitious book that sometimes aspires to more than it achieves. Although the "Aria" legend does beautifully encapsulate and attack the many popular myths of the maverick hero in America, it finally does not seem compelling enough to ignite a young woman with a sustained desire for a man so relentlessly loathsome as Silver. And the novel's use of symbolic weather--withering drought and an apocalyptic rainstorm--asks us to see an epic dimension that the story does not quite deliver.

What it does deliver is the lyrical and devastating portrait of an obsession. We are eager to follow Teresa through puberty and adolescence into adulthood, through her sleeping spells, her bad jobs, her attempts at casual sex, on into the wild landscape of northern California, where the novel's unexpected last scenes are played out. What makes Teresa memorable is not myth or dream but her desire and capacity for liberation from an American family that has been unable to show its children a sane and decent way to live with the past or in the present.