THE LAW of averages decrees that for every dozen performances seen, one or two will linger long enough to register as "an experience". Anything of a higher order is rare, but when it comes, nothing can ever be quite the same again. The ground shifts.The work of Siobhan Davies has always had quality, but the double bill offered by her company of seven at Sadler's Wells had sublime quality. On Wednesday a Dance Umbrella audience was party to a defining moment of dance in the 1990s.

This has nothing to do with a muse descending. Davies and company (for you cannot discuss one without the other) owe their success to sweat, probably tears, and long, hard thought. In 80 minutes of fleet, barefoot dance there is not one predictable moment, not one lapse of invention. You scarcely dare blink for fear of missing something, for the cliches to which most other modern companies are prone have been strangled at birth.

There is no narrative content, yet music, movement and the simplest of settings miraculously conspire to create a potent and specific landscape. Wild Translations takes us into the heat of Africa, yet designer David Buckland's single gesture is a large gleaming fan which ominously rotates above the dancers' heads. The score is Kevin Volans's pulsating string quartet. The dancers' costumes are neutral; there is no suggestion of tribal dance. Yet from these spare elements Davies creates a palpable sense of sizzling equatorial sun, of relief in shade, of swarming insect life and humming human society. She has found a unique way of internalising the external, then pouring its concentrated essence through her dancers' bodies. It is nothing other than a marvel - pure alchemy.

The surprisingly spunky harpsichord music of Scarlatti and the young Matteo Fargion is the springboard for The Art of Touch, urging Davies to a fast, skittering style unlike anything she has done before. No gesture is simple - each has a twist or quirk that gives a spurt to the most fluid of lines. There is quiet humour, there is tenderness; but most of all there is sheer, aching beauty. The duet danced by Catherine Quinn and Paul Old was viewed by more than one hardened critic through a blur of tears. Siobhan Davies was awarded the MBE in the recent round of honours, and the day she opened in London was also the day she went to Buckingham Palace. There is poetic justice.

Increased funding for this year's Dance Umbrella has meant a greater input of big names from abroad. No name comes bigger than that of Merce Cunningham, grandpop-cum-guru of contemporary dance in America, and indirectly, over here.

The show Cunningham brought to Riverside Studios confirms the 76-year- old as the same Sixties swinger he was 30 years ago. Event was billed as a seamless sequence of complete dances and clips from the repertory, "with the possibility of several separate activities happening at the same time". In "Happening" style, this entailed 16 dancers in shiny Star Trek leotards, a giant painting by Rauschenberg, and quadrophonic sound improvised from home-made fiddle, white noise, human groans, shovels, hacksaws, rolled marbles, etc, etc. In true Cunningham style, none of these elements bore any relation to one another. It was as if dance, design and music had come to the party and somehow managed to avoid being introduced.

No aspect of Cunningham's work - stretching back to the mid-Fifties - has been so perplexing as the complete dissociation of dance and music. He has claimed that it allows greater expression to each, and this may be true, but the cumulative effect is to leave the audience crazed and exhausted from splitting their senses in two.

In one sequence, compact groups of dancers launch into lengthy, rhythmic routines, precisely synchronised within each group, creating a complex counterpoint of thudding feet across the stage. Like clocks in a watchmakers ticking at different speeds, it's maddening but mesmerising. Add the musical element and the thing becomes absurd: the synthesiser burbles, someone tears delicate strips from a newspaper, another tunes a radio across wavebands and settles on a distant, crackling "Rock Around the Clock". After a while this is no longer intriguing: it is tiresome and perverse. And oddly old- hat.

Cunningham's Brechtian ideas on staging also seem dated. As the audience settles, dancers limber up in the performing space; others wander on carrying clothes on hangers. During the performance, those waiting their turn sit in full view, distractingly wrapping and unwrapping themselves in blankets and leg warmers as if to underline what vulnerable creatures they are. Cunningham sits with them, motionless, an ancient monument scowling at the stage. It is hard to know whether this is part of the performance or not.

But better an ancient monument in the wings than strutting his stuff on stage. Cruelly bent with arthritis, Cunningham comes on for a solo turn, his heavy, craggy face like a commedia mask, his movements painful and jerky. Fans seem to love this, but he ought to know better. People flock to see Cunningham because he is a piece of history. But on the evidence of Events, his time has come and gone. It is Davies who has just arrived.

Innovation was the very last thing on the bill when the Royal Ballet opened its season last weekend with Swan Lake - the 801st performance of the work at the Opera House. Ivanov and Petipa's choreography is now 100 years old, and Anthony Dowell's production aimed to reproduce as closely as possible what the first Russian audiences would have seen and heard.

The Kirov's Viktor Fedotov, making his debut in the Covent Garden pit, showed how responsive a ballet orchestra should be, nimbly switching the tempo when he detected the slightest discomfort on stage. Yolanda Sonnabend's designs are luscious on a grand scale but never swamp the trademark delicacy of the piece. The corps de ballet - the largest and most elegant flock to be found on a British stage - has never been more exquisite. Its mournful Act IV appearance almost stole the show from the soloists.

Perhaps one day a director will find a better way of staging Siegfried and Odette's death-plunge into the lake. Here, as so often happens, they merely plopped out of sight, as if stumbling down a man-hole. It was a rare moment of bathos in an otherwise glorious performance. Zoltan Solymosi seems to have princely heroism in his genes; Miyako Yoshida, making her debut as a company principal, made a precious Odette, and found a dark glitter in Odile, albeit on a smallish scale. Her debut nerves weren't helped by the all-too-evident disappointment of an audience which had booked to see Darcey Bussell in the role. Bussell, yet again, is nursing an injury.

Merce Cunningham: Sadler's Wells, EC1, 0171 713 6000, today, 3.00 & 7.30pm. 'Swan Lake': ROH, WC2, 0171 304 4000, Fri.