'TWELVE million people just watched you play, " Danny Buch of Red/ATO Records tells Rodrigo y Gabriela as they watch David Letterman gush over their performance on his Late Show. Standing around the bar in Seppi's in midtown New York, watching the show on the TV overhead, the Mexican guitar duo are joined by their Irish manager and a host of American music industry bigwigs. That afternoon they played their unique brand of guitar music on CBS's Late Show to a spellbound studio audience, who clapped and cheered the whole way through their performance.

Watching the show from a backstage dressing room as it was being recorded that afternoon, the couple's stateside representatives . . . independent label ATO Records and Red/ATO . . . were clearly excited. In fairness, they seem an excitable lot at the best of times, all hugs and claps on the back and positivity. But they know talent when they see it and, what's more, they can smell success a mile off.

Legendary ex-Atlantic Records radio plugger Danny Buch has worked with every act from Abba to Zeppelin. "I love these kids, " he says. "I haven't been this excited about an act in a long time."

Kenny Weinstein, who broke the Strokes, is whooping and clapping even before Rodrigo and Gabriela finish playing. "That's the hottest TV performance I've ever seen. Look at that confidence."

The guys from ATO Records . . . home to David Gray and Gomez . . . are hugging in the tiny dressing room, before shushing everyone excitedly as the show returns from commercial break to watch Big Dave plug the album once again. "How could you do that more than once a week?"

Letterman asks in amazement, referring to the couple's frenetic guitar playing as he waves his hand up and down.

The Dublin-based guitarists are from Mexico City. Gabriela Quintero started out her musical career in Mexico playing with three different girl bands at once. Rodrigo Sanchez began by playing drums in his metal band Castlow, which later became Tierra Acida (Acid Earth). The pair met as teenagers at the Casa de Cultura in Mexico City and Gabriela eventually joined Rodrigo's band on guitar, although the two disagree on how that came about.

"I wasn't a fooking groupie, " Gabriela protests in her inimitable Dublin-Mexican accent. "I knew all the songs because I used to practise them every day at home, " she says, as Rodrigo raises a mocking eyebrow. Either way, the two teenagers were united by a love of heavy metal and a desire to broaden their musical horizons.

So, in 1999, they came to Dublin.

Even though Terra Acide recorded an album and were offered a record contract, Rodrigo and Gabriela refused to sign, knowing the limitations of the rock scene in Mexico. Instead they made their living playing bossa novas in the hotel bars of Mexico city before travelling to Europe.

Regulars at the guitarists' live performances will by now be familiar with the story of how the couple ended up in Dublin.

"We met a girl in Mexico and she recommended us to come to Dublin, " Rodrigo begins. "We didn't want to go to London or Paris or Madrid . . . we come from a very big city so we wanted something smaller. . ."

"This girl was living in Ireland at the time, " Gabriela continues, "and she was on holidays in Mexico. So she said to us, 'You should go to Dublin. I have a flat there, you can stay there, I am not using it.' And we were like, wow, we're fooking lucky. So when we got to Dublin we asked the taxi driver to take us to the house and when we got there there was a big note in Spanish on the door and I just thought fook, you know. And it was just like, sorreee, you can't stay here, blah blah blah. . ."

In their first week in Dublin the couple ran out of money and couldn't find anywhere that would pay them to play, so they started busking. "It was fooking great, " says Gabriela. "We were making money and meeting people. . . it was great!"

But then winter came. "I never knew any winter in my life. . . I got very depressed."

So they left Dublin for the warmer winter climes of. . . Denmark. "We had no fooking clue, " Gabriela laughs.

After busking at below-zero temperatures in Copenhagen they made their way to Barcelona's bustling Las Ramblas thoroughfare before eventually returning to Dublin's Grafton Street.

Whilst still busking, singer-songwriter Damien Rice became a big fan of their music and invited them to support his live shows as he launched his album O in 2002.

By 2003 they had released Re-Foc and a year later they released Live Manchester and Dublin. The two albums launched them onto the world music circuit and from there they branched out and began touring Ireland, the UK and Europe. The duo's greatest challenge has been lifting themselves out of the specialist world music genre, something they achieved with gusto in 2006 when their latest offering, the eponymous Rodrigo y Gabriela, was the first instrumental album ever to reach number one in the Irish charts, beating the Arctic Monkeys and Johnny Cash to the top spot.

In October 2006 the couple crossed the Atlantic to take on the unforgiving American live music scene before returning to Europe for a British tour that included a sell-out show at Shepherd's Bush. Then in December 2006 they played four nights at Vicar Street . . . all of which sold out . . . before returning to the States to finish the last leg of their tour.

On their first visit to Philadephia they sold out the 1,000-capacity Theatre of the Living Arts Philly; in Denver they sold out the 2,000-capacity Ogden Theatre; and in Chicago fans queued from 3pm to see their show, with 200 people left outside unable to get tickets. In music industry speak, they have had sell-out shows in all the "main markets", including Los Angeles, New York and Boston. Or, as Gabriela puts it, "We're sorted".

The guitar virtuosi have been confirmed for some of the USA's biggest festivals, including Coachella and Bonaroo. They are currently mulling over the option of doing the Jay Leno show in the next week or two. Their faces plaster the sides of buses in Seattle and their album has been in the top 10 Christmas charts in most indie-music stores across the US. Radio stations across the country are playing their "crazy music", as Rodrigo calls it, and half a million people watched them play 'Tamacun' on Youtube.

Their success in the US has resulted from the same template that ensured their strong following in Ireland, Britain and Europe. Driven by an independent Irish record label, Rubyworks, Rodrigo y Gabriela's reputation is built organically on word of mouth, not massive ad campaigns. For a band with so little marketing push, they are outselling many higher-profile artists and are already playing venues in the US the same size as those played by Damien Rice . . . and their album has been out there for only three months.

But the couple don't seem fazed by the hype. Watching themselves on TV in a New York bar, as millions of Americans tuned in to hear them play, neither mustered as much excitement as the industry people who whoop and hurray and hug, or even the strangers at the bar intrigued to watch the show with two of its guests.

"I am star now, " Gabriela says in a mock haughty voice as she waves her hand dismissively, "bzzzz bzzzz". And she falls into a boisterous giggle. "I've never watched myself on TV before, " Rodrigo observes. "Cool." And that's it.

Rodrigo y Gabriela is out now on Rubyworks