The National: The band who may just have made the year's best album

"We've just got to the point where our shows sell out and there's a buzz," says Aaron Dessner, one of the band's two guitarists and one half of its two sets of brothers. "And when that happens in New York, it happens in a big way. Before our last shows there, one paper described us as 'Brooklyn hipster darlings'. We were like, 'What?! We're the underdogs!' But, in a way, it was like, finally, we're young hipsters! At last, we get to have a backlash."

Formed in 1999, The National released their beautifully orchestrated alt.rock on their own label, Brassland, before their second album, Sad Songs for Dirty Lovers, got them signed to the Beggars Banquet stable, home of The White Stripes. After the stately Cherry Tree EP, The National's first Beggars album is Alligator, released this year to a heck of a welcome. Uncut magazine made it their album of the month. Meg White has been lauding the band, and Bruce Springsteen plays them before he goes on stage. The director Steven Soderbergh has also caught the buzz, featuring them on the soundtrack of his new film.

And how are they liking that? "We weren't surprised as such," says the band's singer, Matt Berninger, "because we thought our first two albums would get more acclaim. But it does feel validating. We wouldn't be doing anything differently if we weren't getting press, but it is nice to see."

That might seem like a languid response, but it's indicative of the streak of richly romanticised outsiderdom that The National turn into a fine art. In part, their songs plunge into the terrain of the party glimpsed from the outside, majoring in the kind of alternately wry, rueful and raucous ruminations on male failings that we haven't heard since the career highs of Jarvis Cocker, Nick Cave and the great grandaddy of them all, Leonard Cohen. To this heady cocktail they add intox-icating dashes of shimmer and twinkle that are very much their own, hinting at city-sized levels of high-in-the-sky euphoria on songs such as "Lit Up", "The Geese of Beverly Road" and "Looking for Astronauts". Marshalling guitars that arpegg- iate gently or leap forward in an Echo & the Bunnymen-like rush, and a chamber orchestra that provides much of the drone and dream of the music, The National soar and shudder vividly.

What initially grabs you about the band is the tension between Berninger's foggy, fell-out-of-bed croon and the acute lyrics, which freeze-frame keenly composed vignettes. In their late twenties and mid-thirties, The National are older than your average breakthrough act, making them well-placed to articulate experience with the awareness that articulacy itself won't prevent you from making the same mistakes. It's not a new vein, but Ber-ninger finds fresh blood in it, giving Cocker and Cave a run for their money on the drunk and reckless mock-machismo of "All the Wine" ("So sorry but the motorcade will have to go around me this time/ God is on my side.") and the splendidly self-lacerating "Karen" ("I lost direction and I'm past my peak/ I'm telling you, this isn't me, no, this isn't me.").

The results sit between nakedly honest confessionals and a more abstract, story-based, even literary kind of songwriting. It comes as no surprise to learn, for example, after asking who the Karen who pops up twice on the album is, that Berninger's girlfriend is called Karin. But Berninger adds that: "very few of the songs are autobiograph-ical. Karin's more of a muse. She's very literary and puts things my way, like the line 'My mind's not right', from 'Abel', which comes from Robert Lowell's poem 'Skunk Hour'."

"We do all that euphoric stuff when you're full of shallow and triumphant vigour," grins Berninger, "but then you bump up against the dumb, weak, human thing. Bouncing the two off each other is something I try to do. I also try to avoid being too 'sensitive male', because that would be just as much bullshit. Describing well a peculiar moment in all its ugly details is, I think, a more beautiful, tender way to talk about something than a rock lyric that's some big, cool-sounding thing. The naked, little stuff is much more interesting."

In that, The National skirt the pitfalls of being yet another New York-based band that succumbs to city-sized hipster posturing. On tracks such as "Lit Up" ("I try to untie Manhattan"), Berninger is more interested in anatomising the pull of the metropolis than simply celebrating it. "There is a lot of New York on Alligator," Berninger nods. "It's impossible to live there and not romanticise it a little. But being from Ohio and not quite being New Yorkers is central to it. Being outsiders, always removed and watching the party through a window."

Rather than rushing to New York as young wannabes, the Nationals drifted there in the 1990s, for work or college. The city fuelled them with a mix of aspiration and old-fashioned cockiness, of the kind that drove non-London bands such as Suede and Pulp to take a chunk out of the UK capital in the Nineties. "You can go out and see good bands every night in New York," says Berninger. "And there are so many people in the city who are pursuing dreams, which is motivating. At the same time, seeing not very good bands playing to a huge crowd was just as motivating, in the sense of thinking, we can do much better than this."

That evening, the band turn that dynamism into this writer's gig of the year. Berninger sings to the ceiling of the converted stable they're playing in, seemingly dragging the songs out of his lanky frame, or croons to his feet with his eyes clamped shut, inside the song. By the time they hit the tension-release button of "Abel", he's all over the stage, as The National channel sibling chemistry, vivid arrangements and nervous energy into something truly combustible. Berninger's right: The National do it so much better.

'Alligator' is out now; The National's UK tour begins at Komedia, Brighton, 14 November (www.americanmary.com)