Collectif AOC, Barbican Theatre, London ***<br></br>Akram Khan, Purcell Room, London, *****

Old tricks, new beauty

The performers of the Collectif AOC are much better than their irritating in-joke name. (AOC stands either for Artistes d'Origine Circassienne – "artists of circus origin" – or for the gastronomic authentication label Appellation d'Origine Contrôlée.) They drop through the air with the slippery twists and jacknifes of Olympic high divers. They stroll up a wall like flies. They juggle. They climb on to each other to form human towers. They erupt into bouts of tumbling, somersaulting break dance. Graduates of France's Centre National des Arts du Cirque, they pooled their diverse skills into a company three years ago and called their first piece La Syncope du 7.

La Syncope du 7 – which translates as "the fainting fit of the seven" – comes to London as a show for adults and children. The opening is mayhem. The large scaffolding structure standing centre stage is a makeshift transparent house filled with clambering bodies. At the front a man swings on a trapeze, his feathery sleeves reminiscent of an angel, his back and forth flight like the distracting, annoying dance of a gnat. What does it mean?

Nothing – and never does. There is no story, only incident and imagery. Choreographed by Fatou Traorè, who comes from contemporary dance , the show aims to pull circus skills into a unified whole. Sometimes several things happen at once, so that while Marlène Rubinelli Giordano entwines herself acrobatically on the moving trapeze, Marc Pareti bounces cross-legged on a trampoline like a latter-day Buddha. Sometimes the business is deliberately silly, provoking laughter among the children (if not the adults). The on-stage musician is part-comedian, part-gypsy in his raggle-taggle outfit. He mixes techno-sounds in his little den under the scaffolding, then moves out to display his percussive skills on different, improvised drum kits. The atmosphere is both anarchic and poetic.

The show's weakness is that after a while all this palls. The same circus tricks are recycled once too often; the dance element is primitive; you long for tighter direction, more cohesion, more invention in combining the tricks. But there are memorable sequences, like the elaborate juggling which gradually incorporates bouncing bodies into the pattern of flying clubs. Best of all is Giordano, the only female acrobat. Small, muscular and feisty, she balances, flies and gives as good as the men.

If the excitement of performance comes in its spontaneous, unrepeatable moment, then kathak, the classical dance of Northern India, must be more exciting than most art forms. With its improvisations and give-and-take dialogues between musicians and dancers, kathak is perilous and fragile, challenging and limitless. For Akram Khan, it is especially close to Krishna, the god who makes mistakes.

Khan may be only 28, but he has more charisma than a fistful of veteran star performers. When he transfixes you with his kohl-rimmed eyes, you feel he could charm a whole pitful of snakes. More importantly, he has blazing talent and vision. In Ronin, the second part of the trilogy he started as the Royal Festival Hall's choreographer-in-residence (he's now associate artist), the vividness of his dancing seems to regenerate kathak's language. The familiar geometries spring out fresh and gleaming; compact and strong, he brings a unique muscular intensity to the virtuosities of kathak.

He also brings a theatricality, not just in the show's dramatic themes, but also in its deliberate framework. His slow-motion entrances, enhanced by Aideen Malone's careful lighting, are an object lesson in suspense and atmosphere. His ankle bells rustle, his travelling body seems to float and dissolve in the semi-darkness. He gradually revs up from curved poses into a proactive dynamic, an arm extending in liquid undulations, the slippery flip of a hand caught like a fish in a spotlight. The oriental lines and angles etch themselves unforgettably, eventually reaching a climax of fast intricacies, arms shooting out like lightning bolts, torso swaying in a brief, drunken backward tilt and inclined head gracefully following.

In Gauri Sharma Tripathi's choreography for the central title piece, Ronin, images evoke the inner turmoil of the Mahabharata's great warrior Arjuna, while the singer Faheem Mazhar tells the story. In Eleven Khan demonstrates kathak's mathematics with a rhythmic cycle of eleven beats, elaborated by dancer and tabla player (Partha Sarathi Mukherjee) in a competitive exchange. The first beat is, as Khan tells the audience, "the sublime", the one to which you always return, the destination to which the tabla player might take one route and the dancer another, but both (hopefully) always arrive there together.

In kathak, Khan says, the elements are interdependent. The dancer can't be separated from the musician, the musician can't be separated from the dancer. That is part of the tradition of kathak, but Philip Sheppard's cello adds a discreetly western component. Like all art, kathak needs to avoid becoming congealed in its conventions. This wonderful show presents kathak in both its traditional and its new beauty.