The False Servant, NT Cottesloe, London<br/>Measure For Measure, NT Olivier, London<br/>Don't Look Back, Somerset House, London

If you're looking for an education of the unsentimental variety, a crash course is available right now. In the National's two new productions, various ingénues learn lessons of a sexual but anti-romantic nature (and I'm not talking about Alan Bennett's History Boys). What is most startling about the 18th-century French playwright Marivaux is how he took commedia dell'arte japes and twisted them, bringing serious nastiness into his protagonists' game-playing.

Thus, The False Servant doesn't end with a happy marriage - though the château in Jonathan Kent's staging is decorated with wedding garlands. The plot sounds, in outline, like a rom-com with echoes of Twelfth Night and As You Like It. A young lady (played by lithe Nancy Carroll) disguises herself as a gallant or chevalier and teasingly woos a countess (Charlotte Rampling). In doing so, the she-chevalier is laddishly bonding with and checking out her own suitor, Lélio. However, Anthony Calf's Lélio is a two-timing, avaricious cad, and her manservant, Trevelin, is no loyal sidekick, either. Played by a sneering Adrian Scarborough, he's a blackmailing rogue who demands sexual favours. In turn, the she-chevalier becomes a cruelly domineering seducer before leaving the countess high and dry, sadder and wiser.

Paul Brown's set is a decayed rococo hall fashioned entirely from glass. Everyone stares in the tarnished mirrors as if self-absorbed, but also estranged by their own duplicity. The costumes, meanwhile, are mid-20th century with Carroll looking like some Noël Coward dream-boy in black tie. Martin Crimp's new translation is scattered with contemporary phrases too, and everybody's materialistic amorality seems horribly modern.

This staging is not as deeply disturbing as Neil Bartlett's recent productions of Marivaux. The threats of violence are never quite convincing, and Carroll glides just too smoothly through the role-playing. However, her androgyny is unsettling, Rampling exudes vulnerability in spite of her swish, authoritative air, and you can feel the irresistible pull the youth exerts on her.

In Simon McBurney's modern-dress Measure For Measure, appearances are again deceptive and more abuse is on the cards. Naomi Frederick's Isabella is scarcely more than a gawky girl as she emerges from the nunnery in her novice's A-line skirt. Going to plead for her imprisoned brother Claudio, she finds Paul Rhys's Angelo - the strict, supposedly saintly state governor - forcing her hand down his trousers.

It has to be said, this production is not McBurney's best work. His use of video footage is uncharacteristically half-baked. The idea of CCTV surveillance is fine - with David Troughton's Duke snooping on cellblock conversations via television monitors. However, if secret cameras in the courtroom are exclusively following Angelo's every move, why isn't his office bugged too? The vague update is similarly irritating: the constabulary are dressed like modern British coppers, and they are executing a guy for getting his girlfriend pregnant... Heaven knows what the next axis of evil will be, but even our sanctimonious PM hasn't got that tough on coitus.

Beyond this, the cast's acting styles are inconsistent with bouts of slapstick sticking out like sore thumbs and exaggerated gestures stuck on otherwise naturalistic performances. Yet, by the end, this production has become riveting, because the key scenes between Frederick and Rhys are intense and suspenseful. Her schoolgirlish naivety is absolutely right as she argues her theological corner with an excitement that's not far off the erotic (rubbing her leg when she's pleased with a riposte). Rhys watches her like a desperately repressed priest, pale as death and quivering. He is, most tragically, tender for a fleeting moment before he spirals downwards into sadomasochism. Troughton is also fascinating as the Duke, an agonised but manipulative greybeard who sometimes seems like a decrepit Godhead. His dubious righting of wrongs leaves one feeling the justice system is frighteningly subjective.

Inspired by the legend of Orpheus's attempt to retrieve his beloved from Hades, Don't Look Back is an elegiac and spooky promenade piece - a kind of haunted installation - devised by Dreamthinkspeak. Leaving you to wander alone around the spiral staircases, dilapidated attics and cellars of Somerset House is a stroke of genius, and designer Naomi Wilkinson - working with director Tristan Sharps - is sensitive to the innate eeriness of this institution. Just by hanging a builder's strip-light in a derelict corridor, she suggests a whole realm of emotional devastation and faint hopes of repair.

This edifice was, of course, formerly the national registry of births, marriages and deaths, and the afterlife proves to be a warren of offices occupied by the undead. You may glimpse a bride vanishing ahead of you, but you meet only somnambulant figures, like Victorian undertakers, who silently point the way. Sometimes, you can only hear typewriters clattering behind locked doors. At another point you spy into a gloomy chamber where a clerk stamps a never-ending stack of certificates. Look closely over the shoulder of the ghoul with the paper guillotine and you find your own name on the list he is methodically slicing up.

Sharps owes a lot to Deborah Warner's promenades in abandoned buildings and some of his living dead aren't born actors, while his filmic installations are occasionally B-rate. Cavils aside though, I was often scared stiff in the pitch black, and the walk through an Escher-like maze of stairwells into the bowels of the aptly named Dead House is truly hair-raising. It smells like the grave and the final vision of the bride - gliding towards you out of the dark, arms outstretched - is one of the most terrifying, beautiful things you'll ever see.

'The False Servant': NT Cottesloe, London SE1 (020 7452 3000), to 15 Sept; 'Measure For Measure': NT Olivier, as above, to 31 July; 'Don't Look Back': Somerset House, London W2 (0870 145 1120), to 14 June