It is a partnership you might never have expected: Sylvie Guillem, great star of western classical ballet, dancing with Akram Khan, virtuoso of the Indian classical kathak style, in Sacred Monsters, Khan’s new production, premiered last week at Sadler’s Wells. Physically, they are opposites — he lithely stocky, with little hair on his head (he makes a point of this latter feature in his narrative, which is why I mention it), she tall and sleek-limbed, with her famous flaming-red hair hanging loose for half the work, then done in a plait for the rest. Yet they don’t look incongruous: their tremendous physical abilities unite them, together with their shared sense of daring. Behind Sacred Monsters, among a jumble of themes — not always cogently expressed — is a quest to make classical contemporary.

At curtain-up, on a striking white stage backed by two huge, curving icebergs (designed by Shizuka Hariu), Guillem stands motionless for ages, holding a skipping-rope made of chain. You wonder why. A female singer (Juliette van Peteghem), with similar hair, functions as a kind of alter ego. Philip Sheppard, composer and cellist, leads the on-stage musicians in his Indian-inflected score. Khan, with bells on his ankles, displays his meticulous technique in foot- and armwork, dwindling to a shiver. At last, Guillem gets a look-in — her suppleness, sinuous arms, fabulous extensions and extraordinary balances exploited in a solo (choreographed by Lin Hwai-min, of Taiwan) in which she seems to be both searching and fighting something off.

There’s a lot of talk in Sacred Monsters (this is rather a preoccupation of Khan’s in his recent pieces) — some funny, but a good deal that’s expendable. Early infatuations figure: his with playing the god Krishna, Guillem’s with Charlie Brown’s sister, Sally, from Peanuts. Well, you live and learn. The best part of this is when Guillem, in a delightful throwaway delivery, reminisces while lying at the front of the stage, manipulating her limbs into extreme positions as a dancer does in warm-up.

As well as the witty moments, there are times when the idea drags. In dance terms, Khan is dazzling as always, with his whirling, darting, madly spinning arms flying solo, but it is the duets that contain the surprises — one jerky, like a dance of dolls, another both playful and wary. He blows at Guillem, sending her tottering off. He butts her in the chest; she knocks him on the head. But after the battle of wills comes tenderness, Guillem clutched round Khan’s body, their arms rippling together in something like ecstasy, to a song like a lullaby. A pity the piece wasn’t so gripping all through.

Earlier at Sadler’s Wells, Bangarra Dance Theatre, from Australia, appeared in Bush, an interpretation — in contemporary-dance choreography by Stephen Page and Frances Rings — of Aboriginal creation stories of Arnhemland. Dreamtime, you call that — though I found much of its 75 minutes more like sleep time.

Peter England’s set designs and Jennifer Irwin’s costumes, evoking the natural world, creatures and Aboriginal art, are often effective (though everything was lit too darkly). A clan woman of brooding aspect, Kathy Balngayngu Marika, presides over the action as an elder. Some sequences drag, or go for little. It would be good to see the strong, attractive dancers — mostly of indigenous descent — in a more tautly organised production with more memorable choreography. When they fall into slumber, it is not before time.

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