Distinctions between modern, pop and classical dance fall in on themselves. Super-articulate bodies move with the fleet grace of ballet dancers - yet have both the weight of modern choreography and its flip nonchalance. There may be a wanton curl of the hip caught up in a rush of classical allegro; there may be an arabesque stretching out of a floppy roll. The structural intelligence at work in the choreography may be making your brain race yet the hairs on the back of your neck will be quivering with the raw thrill of watching bodies moving in space.

As Twyla Tharp's company opens in London today (its first visit in 11 years) the buzz among British dance fans is almost as palpable as when the Bolshoi returned to London in the mid-Eighties. For Tharp is currently making some of the world's most desirable dances. Of all the choreographic talents in New York's lavishly populated dance scene, she is probably its starriest export. Merce Cunningham may be the guru of modern American dance, but Tharp provides the hits and combines hard choreographic invention with glamour and dazzle.

From the beginning Tharp was raised to be a worker, and a star. Her mother called her Twyla because 'she thought it would look good on a marquee'. Schooled intensively in music and dance, little Tharp fell wholeheartedly in with her mother's plans. In her autobiography, published recently in America, she reproduces a scarily rigorous schedule she made when she was only 12: 'Monday. 6 to 6.15am: put practice clothes on. 6.15 to 7.15: ballet. 7.15 to 8: violin. 8-8.30: get dressed, clear room, breakfast . . .'

Throughout Tharp's adult life, art has nearly always remained in first place. Her autobiography chronicles how her dedication and perfectionism put pressure on her relations with lovers, colleagues and friends and helped to break up her marriage. Yet during each period of conflict she seems to have been guided by the same clarity of purpose that shines through her dances. On the subject of her affair with Mikhail Baryshnikov, she said that given the choice between 'a personal relationship with Misha and a great ballet' she would opt 'for the ballet'. When I put it to her that she appears a peculiarly decisive woman she stares at me and says, 'what do you think?'

Tharp's decisiveness and phobia about wasting time make her highly efficient as an artist, but hard work as a woman. When we met in a smart and noisy New York cafe she had just come from a long session with a video company that is looking into putting her archives on to CD-Rom. The next day she was off to work on a film project in LA. She turned out to be an interviewer's dream, snapping out clever, quotable answers with ease. She was also, at times, a jet-lagged journalist's nightmare, killing leading questions dead ('I assume that would be the case/I don't know how to answer that . . .').

Her toughness is partly arrogance - she doesn't have to court anyone these days. But it may also be a hangover from the years she had to fight for status in a male-dominated profession. It may also stem from an impatience with public displays of uncertainty. Tharp has recently made a piece for the Martha Graham Company, a group of dancers dedicated to preserving Graham's work and style. Wasn't the commission, I wondered, an intimidating one? Tharp looks at me as if I were crazed. 'Frankly,' she says, 'no one else remembers that technique as well as I do' (though she studied with Graham for only a year).

Despite her uppish manner, Tharp's autobiograpy is generous and funny in its portrayal of her life. It is not, though, an invitation to personal questioning. 'That's done with, finished, we don't talk about my life.' The point of the book was 'to make the process of dance more accessible. Speaking dance is not some bizarre neurotic thing, it's an extension of our experiences, and to give people a shot at understanding that, I had to give some sense of the experiences that made the dances.'

Certainly the book's greatest achievement is its vivid account of how dances are created. Just as Tharp's arrogance gives way to a co-operativeness when talking pure dance, so, when she writes, she's most passionate and fluent about her choreography - an activity she's always invested with high seriousness. (To a janitor who once chided her for rehearsing on Sundays, she retorted, 'We're a bunch of broads doing God's work').

She refers to her dancers with moving reverence: 'My bodies need to be intelligent, beautiful and sophisticated, capable of the amazing, possessing the great and simple ease that makes you believe one thing: God lives here, too.' And there's a puritanical rigour to her work: 'I've always found it necessity to strip away everything but the most fundamental ways to work - the rest is style . . . . It's very important to work myself physically as hard as I can. The only way to know the truth of a movement is to do it on your own body.'

When she first started working, in the mid-Sixties, she was not remotely interested in mainstream dance. Hers was fashionably austere, performed in silence, the kind 'to which painters came'. In the early Seventies, though, she reneged on purer-than-thou avant-gardism by making dance to music - music with tunes in it like Bix Beiderbecke and Jelly Roll Morton.

By the mid-Seventies Tharp's defection to the mainstream was sealed when invitations came from ballet companies. She made Deuce Coupe for the Joffrey Ballet, which had the company shimmying and bourreeing to the Beach Boys, then Push Comes to Shove for Mikhail Baryshnikov, a love letter to his phenomenal classical technique. Since then she's been internationally in demand.

But for all her experience, dedication and fame, Tharp can't escape the peculiar griefs of her medium. Age, for instance, is starting to curtail her own movement ('One's never happy not to jump as high as one jumped'). Time will also erode her choreography. Despite the fact that she has most of her works on video, she knows 'they will never be danced right again. Every 20 years, bodies are completely different, to say nothing of minds, emotions - it's all bound to impact on the dances.' She's not, though, prepared to agonise over this: 'No artist is well served in thinking what will happen to their works. The best one can hope is that they'll enter the mainstream and people will pull bits and pieces from them.'

To an outsider, Tharp cuts a solitary figure: her son is grown-up, her work veers between long hours alone in the studio and hectic travel. Until 1988 she worked with a permanent group of dancers but the strain of paying them all year round meant she became 'more of a fund-raiser than an artist' and she closed the company down. From her book it's clear that the intimacy she had with those dancers touched her heart, though she briskly denies mourning its loss. 'We all have early family and go out to other lives - it's irrelevent when people spend too much time examining what they once had.'

When Tharp is not working for other companies she takes on dancers for specific projects. The group we are seeing in London will be disbanded and a new one formed for the world tour planned for her 30th anniversary. Courted by dance companies, film-makers, publishers and TV directors, Tharp looks set to run and run. The energy, will and talent that fuel her activities are formidable. But when she mugs an exhausted sigh at the pace of it all, I get one brief glimpse of real tiredness: 'My ideal would be to have wonderful dancers come to me and I'd make work on them and then they'd go away and perform it brilliantly for ever.'

Twyla Tharp Dance is at the Riverside Studios, London, from tonight until 12 March.

(Photographs omitted)