The Hanging Man, Lyric, Hammersmith, London

The suspense isn't killing him, so the suspense is killing him. That's the paradoxical predicament of the protagonist who dangles from a noose but cannot die in Improbable Theatre's new show. In the skeleton of his unfinished Gothic cathedral, Edward Braff, an architect (Richard Katz), does his damnedest to commit suicide. But Death (Lisa Hammond) is peeved that he took her for granted. She leaves him hanging there and goes on strike.

Around this potent central image,The Hanging Man creates a weird setting where the mystical and the matter-of-fact, surreal slapstick and soulful sadness beguilingly collide. It certainly gives a new twist to the idea of gallows humour when Edward's desperate jerkings at the end of his rope are slickly incorporated into a full-company Liberty X dance routine. And the show contains both bravura stunts of grotesque visual humour (religious maniacs sucked, in a vortex of vestments, down trapdoors) and personal revelations (about, among other things, death fantasies) from the actors.

A fable about the difficulty of coping with huge, exposing success (it's that which has driven Edward to despair), The Hanging Man explores our need to acknowledge that we each have a personal relationship (as well as a date) with death. To ignore this is to forget that it underlies our whole lives, which are precious because temporary. That's why Lisa Hammond's no-nonsense Death - as short and stubby a figure as Katz's dangling Edward is long and lanky - was so insulted by the architect's brusque attempt to exploit her. The connection between this pair deepens in mystery and poignancy as Improbable's bittersweet, uncategorisable piece proceeds.

If The Hanging Man focuses on a hero who can't get rid of his existence, Mr Nobody, a new play by Philip Ralph, concerns a figure who can't retrieve his. In a violent attack, Tommy (Niall Buggy), a man in his fifties, lost all memory of who he is. He has since led the life of an uncomplaining tramp. A year later, a woman claims to be his wife. Claire (Maggie McCarthy) is suffocating domesticity in a floral two-piece. The dismay of being told by her that you were a retired small-time businessman called Graham with few friends, no children and a complete set of Tommy Steele records might jam the memory of the most willing amnesiac. Tommy denounces Claire as "some sad old bag who has come out of the woodwork 'cos she doesn't want to be alone any more". But the suspicion builds that there is sadness on both sides and imposture only on his.

All three characters in Jonathan Lloyd's sympathetically acted production are clinging to illusions, not least the former social worker (lovely Patricia Kerrigan) whose ambition to reunite the couple has its origins in the walk-out she has recently staged from her own emotional life. There are glaring implausibilities in the piece, but also moments where Ralph's writing shows real promise. It's a fine stroke to have Claire eventually agree that she has made a mistake and for reasons that allow her to hold on to the idea of "her Graham", while gaining a modest revenge by suggesting that the love of her life would have done something far more extraordinary with his alternative existence than dwindle to a dosser.

'The Hanging Man' (08700 500 511) to 21 June; 'Mr Nobody' (020-7478 0100) to 28 June