The Coen Brothers may not have the strangest film in Cannes this year, but they can certainly boast the drollest promotional giveaway. It's a three-ounce tub of waxy, orange-coloured, sweetly-scented stuff labelled "Dan Men's Pomade". It carries the portrait of a rakishly coiffed George Clooney, looking determined and modelling a convincing facsimile of Clark Gable's moustache.

As promo novelties go, it makes a change from T-shirts and tote bags, and it relates more precisely to the advertised film than is usually the case. In the Coens' new film, O Brother, Where Art Thou?, Clooney's character Ulysses Everett McGill, an escapee from a southern chain gang, wouldn't go anywhere without a dab of Dapper Dan to sweeten his locks. His flight across the deep south is, you can imagine, rather more facetious than the 30s chain gang movies that the Coens take as their model.

Minnesota-born brothers Joel and Ethan are known for liking their bit of fun, and in their latest film, they haven't stinted themselves. O Brother is several films in one: a tale of three desperadoes on the lam in rural Mississippi; a blues and country musical; and, allegedly at least, a rewrite of Homer's Odyssey. Not that they've actually read the Odyssey, they admit. Fortunately, Ethan Coen says, one of the film's leads, Tim Blake Nelson, is a classicist. "I wonder if he read it in Greek? I know he read it." "Yeah," confirms Joel. "Did he?" Ethan insists. "I don't know if he read it in Greek," says Joel. "I know he read it."

"Between the cast and us," says Ethan, "Tim Nelson is the only one who's actually read the Odyssey." There's little point, then, kicking yourself if you can't place all the allusions. The Sirens are easy enough, a trio of singing Amazons doing their laundry in the Mississippi. And the Cyclops is John Goodman in an eyepatch.

Scylla and Charybdis I was less certain about. "Scylla and Charybdis? Where were they?" puzzles Ethan. The whirlpool at the end, surely? "Oh," the brothers chorus, "the whirlpool." Ethan grins pensively. "Oh, yeah, sure, Scylla and Charybdis." Joel says, "It's very, you, usually know selectively based on the Odyssey." Interviewers often lament that with the Coens, there's no point even asking: they don't give anything away.

They have this reputation as tight-lipped enigmatic sorts who make enigmatic films. And yet the films pretty much speak for themselves; they are flawlessly accessible, even if you don't catch all the references to old movies and pulp paperbacks. The only thing that properly seems bizarre about the brothers' work is the breadth of their imagination: they specialise in pinpointing the kind of images and cultural references that are usually outside the remit of contemporary American cinema.

There's nothing that bizarre, if you think of it, about choosing to set a crime thriller in snowbound Minnesota, as the brothers did in Fargo, and having villains who relax by going to see Jose Feliciano in concert; it's just that it took the Coens to think of it. Every Coen film describes a world so thoroughly conceived that each one is its own fictional micro-climate; in a sense the brothers don't really need to add much commentary. Hence, perhaps, the sense that when they give interviews, they are aware of the futility of the venture.

Here they are in Cannes again, sitting in the casino on top of the Carlton hotel, and although they have visited several times in the past (their Barton Fink won the Palme d'Or in 1991), they don't quite seem to belong. Older brother Joel looks as though he's done all the interviews he wants to in a lifetime, Ethan as though he's never done one in his life. Joel seems to have dressed for the part of the hot auteur in town and then let it all get messed up over a rough morning: shoulder-length hair more scrupulously crimped than previously, in a black jacket that could be either very cheap or very expensive; both the beard and the low mutter are reminiscent of Frank Zappa, and he keeps looking absently around the room as if he's wondering how long it is till lunch.

The friendlier Ethan, in a murky brown plaid shirt, with a scraggy beard and a faceful of freckles, constantly grins broadly, occasionally giving a wheezy laugh, and seems to be relishing various private jokes as if they've only just crossed his mind. Despite the grandiose title, O Brother, Where Art Thou? is as downhome and earthy a film as has come out of recent American cinema, although it lacks the lightness of touch of the Coens' best comedies.

It shares its title with the apocryphal movie planned by Joel McCrea's idealistic Hollywood director in Preston Sturges' 1941 comedy Sullivan's Travels (currently on re-release). Sullivan heads out across America to research his serious Steinbeckian hobo drama, only to conclude that it's a far nobler calling to make 'em laugh.

But the Coens' O Brother is not entirely the film that Sullivan would have made. "It pretends to be a big important movie," says Ethan, "but the grandiosity is obviously a joke. It is what it is, it's a comedy. There is a chain-gang interlude in Sullivan's Travels, but that's it." O Brother is another example of the Coens' partiality to period: Miller's Crossing, Barton Fink and The Hudsucker Proxy all explored past decades, and even their last film, The Big Lebowski, had a certain distance, being set in the early 90s as opposed to 1998.

"We tend to do period stuff," says Ethan, "because it helps make it one step removed from boring everyday reality." Their latest film carries a considerable weight of historical authenticity, not least in the soundtrack of vintage southern music - gospel, Delta blues and early country swing - assembled by singer-songwriter and one-time Dylan collaborator T-Bone Burnett.

One of the film's themes is the congruence of pre-war American pop with history and politics, as the errant jailbird trio encounter various real-life characters, among them gangster George "Baby Face" Nelson and blues singer Tommy Johnson, who, like the better known Robert Johnson, was reputed to have sold his soul to the devil in exchange for blues prowess. Another real character is Texas governor Pappy O'Daniel, who would go electioneering accompanied by a "stump band", a music show to whip up popular support. "They'd draw the crowds," explains Joel. "People came to listen to the music and then they'd have to listen to the speech."

The film's southern history, musical and political, looks detailed enough to have been thoroughly researched, but the Coens insist it wasn't. "It's all stuff that to one extent or another we were aware of," Joel says. "It was all back there somewhere and filtered up into the script. We weren't going out and doing research and trying to apply it to a story, it's all much more haphazard. It wasn't like we were trying to create a realistic picture of the time and place so much as an imagined world where all those things intersect - real people and made-up people."

Both are keen that the film shouldn't be taken too seriously, even though for the first time (give or take the socialist convictions of their playwright Barton Fink, and the trendy crypto-fascists in The Big Lebowski) they seem to be focusing on political realities in O Brother. "The political undercurrent of the movie," says Joel, "functions primarily for dramatic purposes, because the politics are frankly pretty primitive. The bad guys are racial bigots and KKK Grand Dragons, and the good guys are the heroes of the movie. So it's all kind of a story thing."

Even so, the film pulls off something of a coup in managing to be more politically flippant than American comedies have managed since Mel Brooks's heyday. The scene where the heroes blithely wander into a torchlit KKK rally might, I suggest to the brothers, strike some viewers as being of questionable taste.

"Taste," says Joel, "has never been something we've worried about." "We're not big on taste," agrees Ethan, his grin broadening even further. "And actually, if you don't pander to undue sensitivities then it ends up usually not being much of a problem. In The Big Lebowski, we dumped the crippled guy out of the wheelchair, and no one seemed to mind that." "Everyone was saying, 'You're going to get a huge amount of mail from disabled people about this'. But it's all in the context of the story, and done by the John Goodman character who's clearly an idiot," says Joel, and Ethan cracks up in laughter.

They are among the most film-literate of mainstream US directors - not indiscriminate movie-guzzlers of the Tarantino school, but scholars of a longer history whose films have referenced Warner Bros gangster pics, Busby Berkeley musicals, and even William Faulkner's fraught Hollywood tenure as a hired script hand.

But the only time they directly used other films as a starting point, the brothers say, was in their 1994 film (probably their least-liked, unjustly so) The Hudsucker Proxy. "We knew we were doing a sort of Capra-esque thing," says Ethan, "but even that was not a specific one of his movies, just the whole sort of' just his thing, right?" They no longer consume films so tirelessly, they admit, largely the result of having children (Ethan has two; Joel has one, with his wife and occasional lead actress Frances McDormand). "We don't watch them together a lot," says Ethan, "and neither of us watches as many as we used to. It's actually gotten more and more hit-and-miss - movies that I planned to see and never end up seeing."

It is generally assumed that the Coens equally represent the presiding genius of their films, but while they share writing credits, Ethan is billed as producer and Joel as director. This means that in Cannes, each film is officially billed as "un film de Joel Coen", although their own production notes specify, "A Film by Joel Coen and Ethan Coen." Confusingly, only Joel's photo appears in the O Brother press kit.

Of the two, it's Ethan who has explored outside ventures. He recently wrote The Naked Man, a film by the duo's regular storyboard artist J Todd Anderson, about a character actor who moonlights as a pro wrestler. The film got a critical thumbs-down. "I thought it was very funny," Ethan says. "I enjoyed it, and not just in a pride of ownership, 'cause it's really J Todd's thing. It didn't get a theatrical release, for reasons I can understand. Its nobody's idea of a big audience mainstream movie."

More prominent was Gates of Eden, the short story collection that Ethan published in 1998. It is frustrating, in a way, because it suggests there's much more to his imagination and linguistic prowess than he is necessarily prepared to put into his movies. More striking than the dry squibs and Chandler parodies are the complex, concise character sketches, and the adolescent anecdotes which hint at the personally revealing movie the Coens have yet to make - although in all honesty, it's hard to imagine them coming up with a screen evocation of a synagogue-going Jewish upbringing in 60s Minnesota.

The next Coen brothers film starts shooting in six weeks. Known as The Barbershop Project, it stars Frances McDormand and Billy Bob Thornton. "It's set in a barbershop and is concerned with the minutiae of the barbering trade in the late 40s." Is that why their distributor has been handing out Dapper Dan's pomade - as a teaser? "It's just a coincidence," says Joel. "There's a lot of hair products in this next film." "Actually," says Ethan, "we use pomade in Raising Arizona as well, as a means of tracking the characters. It's a tired old gag." I scan Joel's faintly slicked locks for traces of his own hair-care product. Would he personally recommend Dapper Dan? "I take no responsibility for that pomade," he says.

 O Brother, Where Art Thou, will be released later this year.