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Dark, challenging and thoroughly strange, “Mad Dog and Glory” is precisely the kind of quirky, personal project that the major studios have long since purged from their production charts.

That it emerged from Universal Pictures is a tribute both to the clout of its co-producer, Martin Scorsese, and to the taste and dedication of Universal production chief Tom Pollock, who has consistently revealed himself as one Hollywood executive who understands the importance of what directors do and is willing to let them do it.

“Mad Dog,” however, has not emerged entirely unscathed. It seems a wounded film, with odd gaps in continuity that suggest an unhappy re-edit, and a wholly synthetic ending that clearly owes more to the dictates of market research than anyone’s honest creative instincts.

Still, there is much here to be salvaged, as there would be of any collaboration among Scorsese, director John McNaughton (of the locally notorious “Henry: Portrait of a Serial Killer”), screenwriter Richard Price (“Sea of Love”), cinematographer Robby Muller (“Paris, Texas”) and principal performers Robert De Niro, Uma Thurman and Bill Murray. The film may not be satisfying as a whole, but there are moments along the way as gripping and inventive as anything American movies have offered in years.

It isn’t the sort of film that allows itself to be reduced to a plot line. Instead, it charts a shifting, unstable, often enigmatic relationship among three troubled characters: Wayne Dobie (De Niro), a puffy, lethargic evidence technician for the Chicago Police Department, whose slow burn style has earned him the ironic nickname “Mad Dog”; Frank Milo (Murray), a Mafia loan shark who finds some vent for his inner hostilities by performing stand-up comedy at a nightclub he owns; and Glory (Thurman), a willowy, elusive young woman who tends bar at Frank’s club and counts herself, as payment for a debt owed by her irresponsible brother, as a piece of Frank’s personal property.

When Wayne, acting with his characteristic coolness and reserve, saves Frank’s life in a hold-up attempt at a neighborhood grocery store, the gangster feels a debt of honor; he invites Wayne to his club, takes him for a drive and a late-night dinner, and presents himself as Wayne’s new best friend.

“I am the expediter of your dreams,” Frank grandly informs him, before sending Wayne his ultimate reward-custody of Glory for seven days, during which she’ll do exactly as she’s told.

The shy Wayne falls in love, and wants to rescue this fair maiden from his new best friend, who has suddenly become his worst enemy.

Where most American movies now feel compelled to make every detail of character psychology glaringly explicit, “Mad Dog and Glory” retains a taste for enigma and ambiguity.

The motivations of its main characters remain deliberately murky, and it becomes difficult to distinguish genuine bids for friendship from cynical power plays, or separate Wayne’s romantic idealism from Frank’s feudal possessiveness-both end in the apparent enslavement of a woman.

As much as Wayne may profess his love for Glory, his deepest bond remains with Frank, who shares his fascination with violence (Frank works his aggressions out as a comedian, Wayne as an amateur photographer of grisly crime scenes). Glory remains an object, a goal (“No guts, no Glory” becomes the mantra Wayne chants to himself), while Frank becomes an intimate, a brother.

For director John McNaughton, “Mad Dog and Glory” isn’t as consistently personal as “Henry” or “The Borrower”-the films he has made as a Chicago-based independent. The movie has his flavor most strongly in its opening scenes, which take place at night on grittily authentic Chicago locations; McNaughton seems to do his best work when he is responding to a specific physical environment, rather than trying to recreate an atmosphere in a studio (the sequences that take place in Wayne’s apartment, an obvious stage set, feel suddenly airless and slack).

Still, McNaughton is able to serve Price’s baroque, highly stylized screenplay extremely well, allowing the touches of dark poetry in the dialogue to emerge without pretension or undue emphasis, and adding a few striking images of his own (one particular shot, representing Wayne’s haunting memory of a lost deer wandering LaSalle Street in the dead of night, lingers long in the mind).

McNaughton also allows Murray and De Niro to find their own wary chemistry, as these two prickly, individualistic performers circle around each other, looking for advantages and opportunities.

In the tradition of great comedians playing heavies (Jackie Gleason in “The Hustler,” Jerry Lewis in “King of Comedy”), Murray achieves a striking, immediate menace, letting the lust for power show behind the laugh-getting urge. De Niro matches Murray’s blustery, extroverted approach with a cool, distanced, interiorized performance-as private and remote as the character he is playing. You have to lean in to hear him.

As the actors’ duel between Murray and De Niro occupies the center of the stage, Thurman’s character is operating in the wings, where she may be manipulating the entire situation to her advantage. In this murky environment, victims can turn out to be victors, aggression can be seduction and tragedy runs very close to comedy, as when Wayne investigates a gangland rubout to the tune of a jukebox spinning Louis Prima’s “Just a Gigolo.”

Also noteworthy are Kathy Baker as De Niro’s lovestruck neighbor (a relationship that remains teasingly implicit), McNaughton regular Tom Towles as Baker’s abusive boyfriend, David Caruso as De Niro’s intemperate partner and Mike Starr as Murray’s lumbering henchman.

“Mad Dog and Glory” (STAR)(STAR)(STAR)

Directed by John McNaughton; written by Richard Price; photographed by Robby Muller; production designed by David Chapman; edited by Craig McKay and Elena Maganini; music by Elmer Bernstein; produced by Barbara De Fina and Martin Scorsese. A Universal Pictures release; opens March 5 at the 900 North Michigan, Webster Place and outlying theaters. Running time: 1:37. MPAA rating: R. Violence, strong language, sexual situations.

THE CAST

Wayne………………………………………..Robert De Niro

Glory…………………………………………..Uma Thurman

Frank…………………………………………..Bill Murray

Mike…………………………………………..David Caruso

Harold…………………………………………..Mike Starr

Andrew…………………………………………..Tom Towles