Elizabeth Peyton can't stop painting celebrities, dead or alive. Robin Muir assesses her strange pantheon of `heroes' and her preoccupation with pop culture
If the American painter Elizabeth Peyton is known at all in this country it will be for her "Britpop Art", portraits of celebrities de nos jours, such as Jarvis Cocker and Liam and Noel Gallagher, and lost souls from other times, too: Kurt Cobain and Sid Vicious, Elvis Presley and Brian Epstein. This iconography has served her well, bringing her considerable attention and success over the past few years, and she is, as a result, no stranger to throwaway hyperbole and the disposable sound-bite - "We can only estimate the scope of Peyton's talent: bigger than a breadbox, smaller than the Matterhorn!" is one recent example, delivered by an American critic. As her subjects have been mostly pop stars, "it's not a huge mystery why people would be attracted to them", she says with a modesty that undervalues her painterly skills.

It would be easy to dismiss Peyton and her world of short-lived celebrity as trivial if she just wasn't so talented. In one of its listings last spring, the New Yorker lost its composure and positively spluttered out exhortations to see the 31-year-old Connecticut-born painter's show. She has exhibited at the Museum of Modern Art, New York, and has admirers in our own art establishment from curators within the National Portrait Gallery to Charles Saatchi, who has one of her paintings - at 7ft 6in wide and 3ft high, an uncharacteristically large portrait of a reclining friend ("He's an artist," says Peyton, "and he's very long").

Critics find it difficult to convey the richness of her style and its peculiar resonance: "punishingly lovely" said one; "slam-bang-cloisonne" and "some of the most achingly stealable things you ever saw", ventured New York's Village Voice; "Flowerlike and fleeting," argued a third, "as if the entire image might fall off the canvas." She had even made it as a footnote in our own OK! magazine, which completes, perhaps, the celebrity circle. Her first book is published next month, "It's mostly a photo-book about Craig [a friend] with some paintings of him and photographs of him and photographs of Queen Elizabeth and Prince Harry." Now she has her first full-scale show, all new work, in London at Sadie Coles HQ and you had better get in line, for, like so many of her subjects, she has legions of fans. Be prepared, too, for their responses: "How does it come about," asked one curator at Nuremberg, "that visitors to an exhibition that contains paintings by Elizabeth Peyton start to cry?"

It is easy to see why she is so acclaimed. Her style is beguilingly naive and her colour sense dazzling, as if the fleeting, boastful notoriety of her pop-starry subjects shouts out for the dramatic and showy gesture or bold in-yer-face paint work (or "brashwork" as Cecil Beaton said of Warhol). But it's not all about surface, for she is a thoughtful painter, with a keen sense of history and of her antecedents, Sargent,Van Dyck, and Hockney, and probably Warhol, too. Whether images of those we recognise or of her friends that we don't, her portraits are beautifully rendered, often miniatures that sparkle like little jewels, vibrant with oranges, lilacs, luscious purples, bleached-blond yellows - colours, as one commentator put it, of "nail-polish intensity".

Though she is shameless in her admiration of her subjects (in interviews she has called them "heroes"), this does not preclude at times serious meditations on celebrity, creativity and destruction and, most of all, the fleetingness of youth and beauty: "With your friends," she says, "sometimes you don't see it because you're with them all the time but you know it's all going to pass." And, despite the ambrosial colours, there is a solemnity to the best of her work. A portrait of Elvis Presley as a young boy with his mother, Gladys and Elvis (1997), a compassionate study of mother-love is, at least in composition, a latterday Madonna and Child; so, too, a picture of Sid Vicious and his mother Anne Beverley. She maintains, however, that death does not interest her: "More the nature of who they are and what makes them so extreme so that they would die young." Vicious remains caught in time for Peyton, her "shining boy child" as Rupert Brooke was to the Bloomsbury Group, another of her subjects, also dead in his twenties. And in a painting of current super-deity Noel Gallager, the religious motifs are unmistakable: "It's Noel coming out of Heathrow when he thought the band was breaking up - he looked dazed, a mess, and he had all the press coming towards him and these two security guards were trying to pull him through. Men on each side of him pulling at his elbows."

If she was not so obviously and touchingly entranced by her subject matter - she appears to paint exactly what she feels - she would be an easy target for accusations of sensationalism. But she is too good for that. Her conversation may look faux-naif, almost Warholian, on the written page, but this gentle, softly spoken woman possesses a genuineness that confounds mockery or disapproval. This is her reply to an interviewer asking if she was paying a tribute to the people she painted: "Sure, they are kind of heroes. They help me. You know, when you have a problem you think: what would Napoleon have done in this case? Or I can think of some stories about John Lennon. You read how he wrote his songs - he didn't know how to write music and he didn't want to know. That's really inspiring, it makes me think I'm OK." Among the other historical "heroes" she has painted are Elizabeth I, Beethoven, "mad" Ludwig II and Lord Alfred Douglas.

And this is her on painting her friends, whom she finds it easier, as Francis Bacon did, to paint from photographs: "I think that a lot of what painting is about, for me especially, is about missing people and wanting to keep them, in a way. So it is sort of important for me to be away from them, to have these photos, to really think about them. I get all confused when they're in front of me. It's too exciting!"

One of Peyton's paintings will not be shown; it is a portrait of Diana, Princess of Wales, which she claims is "too loaded". This is unfortunate, if understandable, for it is extremely good. Taken from a photograph much reproduced last summer, it shows Diana as a teenager reading a romantic novel. "I kept thinking," says Peyton, "that if she hadn't believed in love there would have been no tragedy. She would have continued to be married to Prince Charles. It was irritating that she just couldn't accept it and shut up. I mean, what did she think it was? How could she not know him? She really thought it was all about love and that there are Prince Charmings and all that stuff."

Her painting of Prince Harry (which brought her the mention in OK! magazine) will be on view. It shows him, not long after his mother's funeral, at Arsenal football ground in a bobble hat. "I was drunk one Sunday afternoon in the pub watching this football match, and suddenly on to the screen came Prince Harry. Wow! It was like this angel! An apparition in this crowd of big men."

Pinned down for ever at their most captivating and hyper-real, her heroes possess suffused red lips, faraway eyes and tousled mops of hair. "Believe me," says writer Jon Savage, one of Peyton's most clear-eyed critics with a first-hand knowledge of the Sex Pistols, "Sid was never that cute!" Savage considers Johnny Rotten and Sid Vicious in her double portrait, John Lydon and John Beverley, 1996, dead-ringers for J M Barrie's Lost Boys. This could be said for much of Peyton's oeuvre (there aren't, it must be noted, very many "Lost Girls" here). "I just love the idea," she says of the Gallagher brothers, who look, along with Kurt Cobain, the most "lost" of all her heroes, "that they are these rough boys who did a lot of rough growing up, who drink a lot, swear a lot, take a lot of drugs, but they're writing poetry and singing songs about love. When Liam said `I just want to be happy' after walking out of the US tour, it was just so sweet. "

For the past few months she has been painting for her show at Sadie Coles's Bayswater flat, a situation redolent with atmosphere for a painter with a keen sense of time and place. Lucian Freud painted not too far away, and David Hockney as well, up the road in Powis Square (she has completed a marvellous portrait of Hockney, which should, if there is any justice, end up at one of our institutions - say, the National Portrait Gallery). Close enough, too, to boho Notting Hill and its enclave of rock stars. There, among the video stills, magazine photographs, covers from the music press and old colour supplements that she appropriates for her singular pictures, one of the Nineties' surest and tenderest hands is at work, a master of colour and of the moment

Elizabeth Peyton, 24 February to 9 April at Sadie Coles HQ, 35 Heddon Street, London W1 (0171-434 2227)