OUR FATHERS' SHADOWS By Jack Fuller Morrow. 224 pp. $16.95

JACK FULLER's new novel is about fathers and their children, renewal and corruption, the mystery of life as one generation gives way to the next. Told with power and conviction, the story is set in Chicago, one of the great, old-fashioned American cities -- a city of bright lights, aspiring buildings and jazz, a city that was teaching the world about life and vice before Miami had crawled out of the swamp.

Of course, in literary terms, there are many Chicagos. There's the Chicago of Ben Hecht and Saul Bellow -- Jewish, intellectual, but never far from the streets. Then there's the Chicago of Theodore Dreiser and Nelson Algren -- the stockyards, the immigrant slums -- and not least there's the Chicago of the Irish and Catholic, the special preserve of writers like J.F. Powers and James T. Farrell. It is this last line of descent to which Our Fathers' Shadows clearly belongs. In fact, one of the minor characters is even called Lonigan.

Still, the world has changed a good deal since Studs was growing up on the South Side. Frank Nolan, Fuller's protagonist, is a successful state's attorney, while his wife, Laura, is a composer and pianist -- they are leading a life Studs couldn't have dreamed of. And the crisis in their lives involves survival of a different sort than any Studs ever faced. Frank's father is dying. Worse, he's afflicted with a mysterious disease that the doctors now feel may be hereditary. This news is all the more grievous because Laura's deepest desire is to bear a child -- can they take the risk? But Fuller doesn't stop there. Making these urgencies even more compelling is a terrible crime that Frank is called upon to investigate: a young girl, the granddaughter of a rich banker, has been beaten to death and stuffed in a trash-can. The police feel that they know who did it, but Frank isn't so sure . . .

A dying father, a dead and brutalized child and a terrible fate hanging over generations as yet unborn: these are the elemental materials of Fuller's story. And he's chosen to tell it in a fashion that's equally direct. This is not a subtle novel, but that is its greatest strength. The burden of the narrative is carried by Frank's investigation of the little girl's death, and it propels the book along as powerfully as a story by Ed McBain. Working against the indifference of his superiors, Frank follows his instincts and the clues across Chicago, moving from a rat-infested hotel on the West Side to a ritzy renovation in Old Town. In the end, some readers may complain that Frank arrives at the solution by accident, but that didn't bother me: Fuller defines just the sort of gritty, realistic world where that sort of accident happens.

IN ANY case, it's not here that you expect to find the problem in this sort of novel. The real danger comes when Fuller leaves the main narrative to buttress his theme and establish the subsidiary characters. But despite these excursions, the book never sags. Again, the directness of Fuller's method helps him. It's important that we understand the background of Nolan's family. Fine: Frank's sister simply lets us listen in as she records her diary. And Sam, Frank's father -- a wonderful old eccentric, full of life even as he gasps out his final breath -- leaves his last thoughts on tape, a memento mori for his children and an articulate expression of the novel's themes. As devices, you may call these crude -- but they're effective. Fuller doesn't chicken out on the feelings that led him to write this novel, and says what he wants to say, straight out.

Of course, given the basic nature of the material -- and the fact that almost everyone in the book is Irish -- it's inevitable that the novel's chief flaw is its sentimentality. But you tend to forgive this defect because it derives, not from false feeling, but excess. From time to time, Fuller strains. The most obvious misstep, perhaps, is Jake, Frank's brother. Unwittingly bearing falsely coded DNA, he's been a cipher clerk in Vietnam -- which is pushing things. And when he falls in love with a Vietnamese girl who's infertile as the result of a brutal rape, I'd say he's pushed too far.

Still, for me, the more interesting failure of the novel is its refusal to examine its own assumptions. Think of those Chicago writers I mentioned earlier. They often wrote about the changing of the generations, but in a different way. They were concerned about the conflict between past and present, or how, as one generation surpassed the last, it struggled to find some solidarity with what had gone before. There's little of that in Fuller's book -- instead, generation itself has become the issue. Once it was accepted and assumed; now it's come into question. And Fuller's answer -- that, despite all the obstacles and pitfalls, we must say yes to life -- is not as interesting as why he's posed it in the first place. How come? What are the roots of the urgency he feels?

But no doubt we should be grateful for what Fuller has given us rather than demanding more. Our Fathers' Shadows is a strong, compelling, honest novel, with the sort of narrative drive that would make Elmore Leonard happy -- and should please a good many readers. I missed Fuller's two earlier books. Perhaps the simplest compliment I can give to this one is to say that by the time you read this review, I'll have both of them in hand.

Anthony Hyde, the author of "The Red Fox," is working on a new novel to be called "China Lake."