Nixon's Nixon, Comedy Theatre, London; <br></br>The Relapse, RNT Olivier, London;<br></br>Action, Young Vic, London

Absolute power, total corruption

If Richard Nixon really did agonise over his place in history, as Russell Lees' play speculates, he wouldn't be best pleased that Nixon's Nixon has transferred to the West End. Comic fantasy it may be, but it should still convince the few remaining doubters that the 37th US President and his crony Henry Kissinger were scumbags of the very first rank. Lees' two-hander imagines what might have passed between the two men during a three-hour meeting they held in the White House on the eve of Nixon's resignation. Lees keeps the details of Nixon's nemesis, Watergate, to a minimum, and asks instead: how does absolute power feel, and what's it like to lose it?

Charles Towers' production, a hit on last year's Edinburgh Fringe, takes time to hit its stride. Its first half would work as well on radio. Keith Jochim's lolloping, dimwitted Nixon is begging his Secretary of State to haul him out of the Watergate mire. Tim Donoghue's pursed Kissinger, dancing attendance on a man he scorns, has his own worries: can he keep his job in the next administration? It's a power struggle between two men unused to being powerless. Eager to re-enact his moments of glory, Nixon asks a reluctant Kissinger to impersonate Brezhnev, Mao, JFK. As their long, drunk night of the soul nears its end, the pair devise a scheme that might save their skins: provoke an international crisis to distract attention from imminent impeachment! (Bill Clinton knows the routine.)

It's with this demented finale that Nixon's Nixon pays its dues. Jochim and Donoghue build up a crazed head of steam as they play out their fantasy of global destruction on and around the Lincoln Sitting Room's plush tables and chairs. "Burning villages! Rape! Pillage!" screams the President. Lees describes two men capable of understanding only power – "better a ruler in hell," says Nixon, "than a servant in heaven" – and asks us: are we wise to give our politicians so much authority to abuse?

Or our theatre directors? National Theatre supremo Trevor Nunn has been accused of abuse of power himself recently. At least The Relapse, unlike My Fair Lady, won't further fill his bloated coffers. Nunn gives the 18th-century comedy a jolly revival that boasts a select few superb performances. Alex Jennings pitches in a comic tour de force as the monstrous egotist Lord Foppington. His powdered face pinched, his precipitous wig teetering, Foppington is of the breed of dandy who pauses, mid-swordfight, to admire his opponent's "nice cuffs". Jennings revels in the role, pronouncing its catchphrases ("stab me vitals!") and snooty mots injustes in an improbably elongated drawl.

The play is another Restoration-era (almost) demolition of romance and marriage, in which Nunn has cast his own spouse, Imogen Stubbs. "No man worth having was ever true to his wife," says Claire Price's Berinthia, the bright-eyed, deceptively demure young widow to whose tune a roundelay of adultery and sexual ambition revolves. Meanwhile, in the second of two concurrent plots that frustratingly never converge, Foppington's dashing brother gazumps the Lord in the race to ensnare a country wife. I found the play's callousness rather glib: Nunn has foregrounded spectacle and fruity comedy, but failed to extract performances from either Stubbs or James Purefoy as Loveless to suggest that adultery actually matters. We're treated to several show-stopping knees-ups and brawls against Sue Blane's period theatre backdrops, but it's the star turns – that's Jennings and Price, Maxine Peake as Foppington's loveably unspoiled bumpkin bride, and Edward Petherbridge as a nit-ridden matchmaker – that command attention. The Relapse won't stab your vitals; it might just stir them.

A few hundred yards down the road, the Young Vic's season of American drama continues with the seldom-staged Action. This early Sam Shepard play imagines two men and two (fairly incidental) women confined in a remote building, in a snowstorm. ("It's freezing outside," the first-night audience heard, as we sweltered in our seats.) As the characters enact various portentous rituals – Jeep mechanically dowses his hands in a bucket; Lupe flicks through a book in search of her lost page – we gather that this isolated outpost denotes their existential angst. They're citizens of an America that's lost touch with the simple freedoms of its frontier origins. "What's community?" they ask one another. But answer comes there none.

The quartet don't develop recognisable relationships, and there's no story as such. This wilful obliqueness can make for frustrating viewing. The evening comes alive at the least likely moment, when John Sharian's Jeep fillets a fish with his switchblade. Suddenly, there's an action to complete; a challenge to surmount – something inescapably real happening onstage. Sharian is a dead spit for an Apocalypse Now-period Marlon Brando and has the presence to match. In his bear-like frame, the brooding energy of Arlette George's production resides.

Nixon's Nixon: Comedy, SW1 (020 7369 1731), booking to 15 September; The Relapse: RNT Olivier, SE1 (020 7452 3000), in rep; Action: Young Vic, SE1 (020 7928 6363), to 11 August