The second Women of the World festival -- WOW -- opened on the South Bank last night with a solo show, Beside the Sea, a performance that hardly fitted the subtitle of "celebrating the formidable strength and inventiveness of women." Instead, it was about a depressed mother killing her children.

But what a performance this was: Irish actress Lisa Dwan delivering an 80-minute tour de force as the depressed, unnamed anti-heroine of Veronique Olmi's remarkable French novella, translated by Adriana Hunter and published by the brand new Peirene Press.

And, for now, your only chance of seeing it, in Irina Brown's superbly sensitive production, is to hie thee hither to the Purcell Room this very Thursday night. Thereafter, I suspect the piece, and Dwan's performance, will become a festival fixture around the world.

This modern Medea takes her children to the seaside and has no intention of bringing them home. Her boys are nine and five years old. In the brown boarding house by the sea, the mother watches them sleep. "Where does everybody go? Is there a kingdom of dreams?"

A meditation on sleeping and consciousness can easily segue into thoughts of death and murder, and there's nothing unreasonable -- this is what is so shocking -- in what Dwan's character does. She is saving her children from the world. She gave them birth. She has that right.

Except, of course, she doesn't. Fleetingly, we learn she goes to a health centre. The boys have different fathers. She thought she'd make them whole in death. Instead, they lie on the bed in the hotel with their backs to each other.

Dwan, an actresss of real fibre, looks so frail and so, well, pretty, in her page boy haircut, white shift and brown boots, melding into a harsh landscsape of pebbles on a long white drape. How could such horrors be done?

As became clear in an after-show discussion, her Irishness somehow enforces the "nowheres-ville" and everyday application of the story. Because we read about such cases in the newspapers all the time. Most male child murderers are violent abusers, too. Most female child murderers are merely, perversely, altruistic. This show explains why.

Dwan even executes moments of transfiguration, climbing on the bed, or the cafe table where she takes the boys on their "day out," as if pleading her own case for the defence. She's in a trance, almost, occupying a higher plane where such things might happen and premeditated murder might have a logical justification.

Her scream at the end is one of the bravest physical expressions I've seen in a theatre for a very long time. And it links directly to Dwan's performance at this same WOW festival last year of Beckett's Not I, in which she was all mouth, tumultuously, for a record-breaking nine minutes and fifty seconds.

It's great to see the rest of her this year, though admittedly that's not an awful lot. She's an elfin, fragile creature, and that makes the performance of the desperate mother all the more moving. She's so much like her own sons. She's killing them both, and herself, because she sees herself in them, too much.

Jude Kelly was on hand to welcome the WOW guests who included actress Diana Quick, director Fiona Laird, producer Colin Watkeys and writer Stephanie Merritt. Their presence brightened the otherwise cheerless environment of the Purcell Room, with its school hall furnishings and black plastic seats, not to mention the ludicrously overpriced and impersonal bar.

No wonder the place, and its neighbour, the Queen Elizabeth Hall, sprog infants both of the Festival Hall next door, is a concrete wilderness for most people but a weird haven for classical music fiends who don't give a monkey's about style, setting or aesthetic beauty.

WOW continues over the weekend with visits from Annie Lennox, Sinead O'Connor, Jo Brand and Sandi Toksvig. No suprises there, then. But Lisa Dwan will be matched, surely, on Sunday, by a drop-in matinee from Linda Marlowe and her stunning performance of poet laureate Carol Ann Duffy's The World's Wife. Now, that really does give back to women the balls Lisa Dwan's character so tragically lacks.