When Noel Coward fought the flu aboard a tramp steamer one weekend by writing Private Lives for his great friend Gertrude Lawrence and himself, he may have thought he was tossing off a mere bagatelle. What he wrought instead is a comedy that represents the epitome of 1930s sophistication, as proven by the new Broadway production of Private Livesat the Music Box Theatre, with Kim Cattrall and Paul Gross performing sleekly enough to suggest they're a modern-day Noel and Gertie.

Indeed, the production, directed debonairly by Sir Richard Eyre, is so close to ideal that spectators caught caviling should be led to a corner and forced to hunker there until they come to their senses.

The three-act play (presented here with one intermission) concerns ex-spouses Amanda (Cattrall) and Elyot (Gross), who by sheer and serendipitous accident discover that on their second honeymoons -- she's with stuffed-shirt Victor (Simon Paisley Day), he's with gushing innocent Sybil (Anna Madeley) -- that they are occupying adjacent Deauville honeymoon suites.

While their song, "Someday I'll Find You," floats up from the hotel band, they realize they still crave each other and give in to their sexual and psychic longing. They hastily depart for Amanda's Avenue Montaigne flat, where they spend act two fighting, kissing and making up -- and act three being stalked by Victor and Sybil.

By play's end, their idyll, which includes the arrival of baffled French cleaning-lady Louise (Caroline Lena Olsson), reaches the only amusing ending Coward believes they've earned. Indeed, there are few romantic comedies -- on stage or screen -- where the principals are so fated to be mated and frustrated yet remain incompatible.

Playing the intense and self-absorbed lovers, Cattrall (slim as a lily stem) and Gross (suave as the silver cigarette case he carries) are the overflowing volcanoes of molten intelligence, humor, glamour, impetuosity, rancor, unpredictability and desire that Coward created.

Madeley -- who bears enough resemblance to a young Cattrall that it seems Elyot has attempted to remarry his first wife -- is a compact bundle of expectation and chagrin. The mustachioed Day wields his pipe and furrows his log face with comic acumen. Olsson, speaking only French, gets laughs in that language.

All is not complete perfection. During the second act, when the star-crushed lovers bicker, despite their first-act pact to halt such contretemps when one of them says "Solomon Isaacs," Coward throws in at least one too many flare-ups for the work's own good.

For this version, there's also something off-kilter with the large-scale Paris flat Rob Howell has designed, featuring a high ceiling that mysteriously contains a huge comma cut-out and a wall mural on which ducks frighten a school of fish. On the other hand, there's nothing amiss with Anna Ledwich's stylish costumes, or the splendid performers who inhabit them!