An agent who secretly infiltrates a rival organization is usually called a mole. But in “The Departed,” a gritty, crackling cops-and-robbers contest in which both sides of the law have a man burrowed deep in enemy turf, that term seems indecently polite. Moles are known as rats. More often, effing rats.

This is a Martin Scorsese film (scripted by first-time Scorsese collaborator William Monahan), as heavily flavored with the director’s favorite modifier as “Goodfellas” and “Casino,” and set to the same jubilant beat as those mafia pictures: strings of obscenities, staccato bursts of gunfire, the sounds of blunt objects meeting flesh and bones. Like its milieu, Irish-Catholic Boston, “The Departed” has plenty in common with the mean streets Mr. Scorsese has trod before, without the watershed setting or the whiff of Grand Guignol that complicated the mix in his last violent romp, the period piece “Gangs of New York.” It has plenty more, too.And for both these reasons, it’s awfully fun to watch.

The same could be said for the two informers at the center of the story, which is borrowed from the 2002 Hong Kong policier “Infernal Affairs” and might have been plotted on a mirrored axis. Ostensible gangster Billy Costigan (Leonardo DiCaprio) and ostensible police sergeant Colin Sullivan (Matt Damon) are both the opposite of what they appear to be. Billy, a strung-out undercover cop, puts his life on the line cozying up to Boston’s biggest crime lord, Frank Costello (Jack Nicholson), and leaks the cops the details they need to bust him. Colin, the spit-and-polish young star of the special investigations unit, coolly foils every sting.

Both sides discover, at about the same time, that they’ve got a traitor in their midst, and take measures to flush him out. But while Frank starts to doubt Billy’s loyalty, Colin actually makes himself more secure at headquarters. He earns a promotion that lands him in a new glass-walled office and seemingly beyond suspicion, and starts dating a smart, pretty staff pyschiatrist (Verga Farmiga) who’s been trained to know a policeman’s darkest secrets. She doesn’t suspect a thing.

Things are actually less volatile in Frank’s gang than within police ranks, which are aboil with internal rivalries and the hot tempers of the (mainly Irish) personnel, in particular Dignam (Mark Wahlberg), Billy’s liaison to the inside. Dignam is a bloodhound dedicated to putting Costello away for good, but — as becomes hilariously clear in several abuse-ridden briefings — he does not work well with others.The bad guys, on the other hand, are pretty much run by Frank — with occasional reinforcement from his “associate,”Mr. French (Ray Winstone),a swarthy type who lacks the Gallic refinement his name might suggest. As things progress, you start itching for these well-matched sides to get it on. Eventually they do, in a shootout that explodes so abruptly it will make your jaw drop.But that is just the beginning of the end.

“The Departed” has too much pizzazz to bear real comparison with “Mystic River,” Clint Eastwood’s tragic tour de force about the working-class back lots of Boston. But like that film, it does burden a dream cast of mostly non-New England origin with the arhotic regional accent. Is it as convincing as a game of undah-cuvah cawps and rawbbahs? Not entirely. For Mr. Wahlberg, a Boston native, it’s a piece of cake; Martin Sheen, in the role of a gentle police captain, manages it gracefully, while Alec Baldwin, playing a dryly buffoonish one (and once again proving himself a master of straight-faced humor), exploits its full comic potential.

Mr. Baldwin’s character represents just one of the film’s many divergences from “Infernal Affairs,” a slick cat-and-mouse thriller that is often credited with revitalizing Hong Kong cinema but hardly warrants rote adaptation. “The Departed” does away with that film’s suite of sentimental flashbacks and adds an extra hour of runtime to tease out the protagonists’ secret identity crises. Mr. DiCaprio (playing an orphan, once again) artfully shows Billy’s nerves fraying to reveal his core of vulnerability, while Mr. Damon lets an anxious sycophancy peek out from behind his Kevlar composure. Mr. Nicholson is given generous opportunity to play Jack Nicholson; not much to complain about there.

Onto backdrops of federalist architecture and exposed brick, Mr. Scorsese sketches his own allegory of class competition. Billy and Colin are equally canny young men, one firmly in the clutches of a bruised-knuckle caste, the other striding, with a grin on his face, into white-collar success. If “The Departed” were a 19th-century novel, it’s a safe bet Colin and Billy would be revealed in the end as long-lost brothers. As it is, the film does more than suggest this pair of blond, snub-nosed impostors are kin, of a sort: They share a dubious father figure in Frank, the louche, ball-busting king of the hill, and, before you know it, they’re sharing a girlfriend, too. As in a good deal of the Scorsese canon, she isn’t given a whole lot to do, other than feebly attempt to get into the mens’ heads. (Frank sneeringly refers to her as “Little Miss Freud.”)

Confessions don’t come easily in this familiar Scorsese landscape of lapsed Catholicism. The clergymen who show up in cameos get no closer to extracting penitence than Ms. Varmiga’s comely psychoanalyst: It seems a fellow simply won’t come clean until he’s got a bullet in him. But it’s not whether you lie that makes you good or bad, it’s why you do it, and Mr. Scorsese, as usual, makes sure that simplistic (or outdated) definitions of virtue get their due: Priests are implicated as child molesters; a glass-framed portrait of the Virgin Mary proves handy for cracking a stoolie over the head.

It’s a nice touch of irony to christen this film “The Departed,” a soothing, spiritually flavored euphemism that a cop employs, quite malapropos, at one point to describe someone who got knocked off. Calling the guy “the departed” may be good manners, or protocol, or whatever. But there’s really no place for that kind of talk here.