Jimmy Stewart would never have been able to cope with the giant rabbit that haunts Donnie Darko's demented waking nightmares. This thing is no friendly cottontail like Harvey. It's a macabre-looking monster with a hard, malformed pewter face, snaggled teeth and ominous blank eyes without pupils.

This rabbit's name is Frank, and he may or may not be a figment of the heavily medicated, intensely tormented imagination of the delusional teenage boy at the center of the engrossingly bizarre, mind-bending fringe film "Donnie Darko."

Whatever Frank is, it's his hypnotic influence over the eerily vexed title character (played by Jake Gyllenhaal) that launches him into a surreal labyrinth of increasingly esoteric encounters, starting the night Donnie sleepwalks away from his parents' house, seduced by the chilling sound of Frank's resonating, semi-synthetic voice. The world will end in 28 days, five hours, 52 minutes and 12 seconds, the diabolic bunny intones.

When Donnie returns home the next morning, a 2,000-pound jet engine has fallen -- from a plane the FAA cannot account for -- demolishing the bedroom he'd have been sleeping in if his apparition hadn't drawn him into the darkness. Clouded by mood-stabilizing drugs prescribed by his baffled shrink (Katherine Ross), Donnie embarks on a psychotropic quest to find meaning in this coincidence of his continued existence -- and all the while he's very much aware that the clock is ticking on Frank's cryptic prophecy.

Written and directed by 26-year-old Richard Kelly, this unsettling, darkly funny bit of psychological science fiction plays like a comic book rendition of a David Lynch film. The story's timeline of skewed reality folds in on itself as Donnie falls more deeply under Frank's influence. The rabbit continues to turn up in his mind, compelling him to misanthropy, capricious vandalism and worse.

Gyllenhaal is completely absorbing in this turbulent, abstractly sympathetic role. A young actor of remarkable range (he gave heartfelt and earnest depth to the all-American boy in "October Sky," and nuanced yet screwball naivete to the hitchhiking convalescent in "Bubble Boy") he conveys brilliantly, through glowering eyes and defensive body language, how Donnie is separated from normalcy by a thin, transparent, impenetrable membrane of overwhelming neuroses and psychoses. His performance is the key to the film's potency because every increasingly anomalous development is filtered through Donnie's point of view, as Gyllenhall carefully unfurls one warped layer of personality after another.

Meanwhile, our anti-hero crosses paths with a passel of disturbingly sanctimonious eccentrics, like the cult-ish self-help guru (Patrick Swayze in an unsettlingly Stepford-esque performance) whose program of emotional extremes is being taught as gospel in Donnie's archconservative private school. Frank soon surfaces again, telling Donnie to burn the guy's house down. He skips out on a date with a pretty, curious classmate (Jena Malone) to do it.

Being a first-time screenwriter and director, Kelly's narrative is sometimes a little sloppy. The shrink's dialogue is pure plot device, some characters are overly cartoonish, and one pivotal story element feels tacked on for convenience. But his vision is unwaveringly vivid and his technical skills are impressive. In one silent tracking shot that speeds up, slows down, encircles and zooms, he establishes a comprehensive understanding of the atmosphere at Donnie's school -- from power plays by the secretly coke-addicted school stud to the professional frustration of Donnie's favorite teacher, an unorthodox lit instructor (played by producer Drew Barrymore) who is being censored by the school board.

As Donnie begins to form a theory about what's happening to him, his delusions manifest themselves in more and more unearthly ways. He starts seeing liquidy extensions of people's spirits expanding from their bodies (his own soon leads him to his parents' bedroom and goads him to steal a gun from the closet). After he is given a book called "The Philosophy of Time Travel," all the film's outlandish threads come together in a portentous twist of temporal physics that turns the idiosyncratic world of "Donnie Darko" in on itself in ways that boggle the imagination.

In some ways, "Donnie Darko" is like a 21st Century Brothers Grimm tale. In others it's a commentary on the social politics of the 1980s (the movie takes place during the '88 presidential election). It could also be the evil, parallel-universe twin of the jaunty teen films of that era. Looking at its corkscrew narrative, it could be seen as a parable about sacrifice and second chances.

I'm not sure just how to summarize "Donnie Darko," but I can tell you it's one of the best, most challenging, most intellectually cagey films of 2001.