Two weeks ago some humourless Texas policemen wearing reflective aviator sunglasses busted Matthew McConaughey in his own home near Austin. Called out one night on a neighbour's noise complaint, they found the actor thrashing around in a happily demonstrative naked bongos session and hauled him off on a clutch of dubious charges - including possession of marijuana (now dropped through lack of evidence).

McConaughey set the scene with his customary, sunny-side up smile as he wolfed down a huge plate of eggs and toasted ham sandwiches in the first two minutes of our interview. Sitting almost upside down in his chair, his feet waved in the air like a kid's, watching television.

"It was full moon and ah had the doors to the garden open," he explains in his mild Texan drawl. "We were just jamming, man, and all of a sudden there was this light in mah face." They say novelist Jack Kerouac was crazy for the bongos (witness the sale of his broken set at a recent Sothebys' sale) and used to drum routinely on everything in sight in a constant percussive piece of dialogue with himself. McConaughey also possesses a not dissimilar hyperactive, live-wire masculinity to that beatnik guru; he also feels the need to drum, pound and generally feel the rhythm on everything that crosses his path.

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He demonstrates this constant itch by pattering his palms against his well-toned stomach and claiming this was the original musical instrument of mankind. This man surely loves to drum. I began the interview under the fond illusion that McConaughey might be a little prickly on the subject of bongos, nudity and out-of-control behaviour. But I felt that a little sensitive questioning might bring him to talk about it. How wrong I was: bongos, bongos, bongos were all he really wanted to talk about.

"Was ah playing bongos buck naked at two in the morning?" he asks with a smile as big as the Lone Star State. "Yes sir, I was, and ah done it 500 times before."

OK, so he likes bongos. A lot. He likes to have fun. But I got boring on him. In stark contrast to these warm feelings about percussive skinny- dipping, when confronted on the issue of his upcoming movie U-571 (which re-writes the history of the Second World War by having an American commando unit capturing the famous Enigma code machine off a German submarine, when actually the British captured it before the US even entered the war), he was extremely uncomfortable with the idea of offending us Brits and clammed up tight. OK.

Any mention of his "ex" and Texas neighbour Sandra Bullock, whom he famously dumped, also brings up a weirdly blank face. OK. And don't expect too much insight either into his very latest movie, EDtv, in which he takes the role of the regular guy who stars in a 24-hour real-time cable show of his life.

The McConaughey thing exists on a purely instinctive level. Possibly McConaughey himself doesn't quite understand it. Steven Spielberg thought highly enough of his abilities to recruit him to a key role in the slave drama Amistad (1997), where he plays a young lawyer who presumes to defend "the Negro". Other top-name directors have gone on record, trying to pin down what makes him so likeable and watchable on the screen. "I don't know anyone like him," observed Joel Schumacher (who directed him in A Time to Kill in 1996). "There's an innate integrity and elegance about Matthew." Richard Linklater - who directed him as a dope-smoking dude in the totemic slacker movie Dazed and Confused (1993) - also noticed his "sincere, truthful quality" and how he "knows who he is". John Sayles, who recruited him for the big indie hit Lone Star (1996), also liked his "strong presence", adding that "there is nothing histrionic about him".

But despite his price tag of $1m a movie and this roster of superior directors seeking him out, there's something about McConaughey's career that hasn't quite ignited. His great breakout movie, A Time to Kill, really went nowhere; Contact (a tricky romantic lead with Jodie Foster), underperformed at the box office, as did Amistad; and, it has to be said, EDtv, a perfectly nice little Ron Howard movie which had the misfortune to go up against The Truman Show and lost out big-time (Howard, it is reported, is horribly bitter about this). So it's not surprising that McConaughey is developing eight of his own projects "out of mah own pocket" to find that elusive, cracking big movie he really needs - including an Evil Knievel biopic in which he says he'll do some, but not all, of his own biking stunts. "Ah'm wild, but ah'm not foolish," he drawls.

The most weirdly fascinating thing about EDtv is possibly the casting of Woody Harrelson as McConaughey's older brother: the two have such a strong physical resemblance it's really quite uncanny. This close relationship seems to have spilled over into everyday life, and the day I met McConaughey in London was the day before he flew out to New York to catch Harrelson's new play. "Woody's got one of the healthiest minds, body and spirits that ah know," McConaughey opines. "Ah haven't seen him for a while and ah miss him."

Woody - you'll not be surprised to learn - was one of the first on the phone after news of the bongos arrest broke in the world media. But it's probably just as well the Travis County attorney, who dismissed the marijuana part of the charges last week, didn't get wind of Woody's subsequent gift to the oft-naked drummer: a hemp sweater.

Woody Harrelson is, as you may have heard, quite a fan of things hempen. And McConaughey likes nothing better than hanging out at Woody's eccentric (and very LA) "oxygen bar" in Beverly Hills where he goes for a puff of pure oxygen with King Hemp himself. Meanwhile, Woody's new-found little bro' shows no signs of backing down from his right to make a racket: he boasts of an ownership of "bongos, congas, washboards, harmonica and guitar", and insists on his right to invite Cameroonian drummers round to his house to party.

Despite the rather absurd aspect of his arrest, and the lurid reporting of its circumstances, McConaughey comes across as extremely knowledgeable on the subject of African percussion and may one day "make a documentary on the subject". US lovers of their own eccentrics beware. Claiming he will celebrate his reunion with Woody with a bongo jam, McConaughey leaves me in no doubts about the depths of his feelings on disrobed drumming. "If ah can't play bongos naked in mah own home, man," he declares, "I'm gonna leave the country."