Once in a great while a play comes along that is so extraordinary it actually alters the experience of theatergoing. The terrific production of Alan Ayckbourn’s 1982 play cycle “Intimate Exchanges,” now at 59E59 Theaters, is that kind of phenomenon. “Intimate Exchanges” makes people want to chat up the stranger sitting next to them. It compels audiences to return night after night, to see the same beloved characters in another of the eight episodes of which it is comprised. In short, it inspires a rare sort of affection.

Initially it’s the elaborate structure of “Intimate Exchanges” that excites the audience’s curiosity. The play’s first scene — in which a woman decides whether or not to smoke a cigarette — branches out into one of two possible scenes. Each of these, in turn, produces two new options. In all, there are eight possible permutations of “Intimate Exchanges” (with two codas each, for a total of 16 distinct versions in all). Each night’s sequence is predetermined, and both audiences and actors arrive at the theater knowing which version will be performed. But there is still something exciting in watching the structural conceit play out — particularly since two astonishing actors play all 10 of the characters.

But 15 minutes into the play you’ll have all but forgotten the crafty structure. By then you’ll be deeply engrossed in the lives and loves of these vivid characters, attending them with rueful laughter and genuine fascination. After half an hour, you may find yourself forgetting that there are only two actors in the cast. And by intermission, you’ll be rehashing events with your neighbor and making plans to see another installment.

You will want to come back to see what other courses Celia Teasdale, the local headmaster’s neglected and fretful wife, might take with her husband Tobey, a hard-drinking cynic with a dry wit. And you will want to find out what transformations might be possible for the Teasdales’ cheeky household helper, Sylvie Bell, and Lionel Hepplewick, the school’s affable, non-too-bright groundskeeper. You will find yourself wondering about other potential developments in the strained marriage of the inept, earnest Miles Coombes and his needy wife, the wild and unsteady Rowena.

That you will come to care so deeply about these characters is a testament to the remarkably fine-grained portraits etched by the production’s two actors, Bill Champion and Claudia Elmhirst. Working with little more than a few wigs and costume changes, the actors — through posture, accent, body language, and all manner of subtle distinctions — give us 10 thoroughly differentiated people. Their achievement is nothing short of dazzling.

Yet ultimately what makes “Intimate Exchanges” so irresistible is the bountiful imagination — and the profound humanism — of its author. Mr. Ayckbourn has a biting wit and a sober eye, but he also has a generous heart, and it’s that heart that suffuses these plays with an uncommon warmth. His writing implicitly asks us not to judge these characters, but to consider their frailties, their limitations, their longings, their fears.

“Intimate Exchanges” has sometimes been mistaken for light fare — a comic entertainment for and about middle-class Brits, set in a distant suburb of London. The frequent sitcomlike setups and the abundance of crackling one-liners add to this impression.

But just because Mr. Ayckbourn can write witty repartee and slapstick scenarios with the best of them doesn’t mean that his play doesn’t have deep roots. The humor of “Intimate Exchanges” is drawn from some of the most distressing corners of the human heart. Characters lose hold of their own feelings as they rationalize away the hurts inflicted on them, drifting dangerously far from the selves they once most cherished. Sometimes, they trade one failed affair for an equally doomed one, living on scraps of pathetic affection. Sometimes — and with breathless excitement — they break free of the painful ties that bind them to the wrong lives.

All of it happens in a series of one-on-one encounters — the “intimate exchanges” in which, amidst much humor and pathos, they intentionally or unintentionally strip away select pieces of armor and ask the other person for understanding. As in life, they don’t always get it, but when they do, it feels like a small but glorious victory, not merely for them, but for the lot of us.

Such a formidable stage production is seldom attempted and not to be missed. Tim Luscombe and Mr. Ayckbourn, who co-directed, have made the best use of minimal sets, lighting, and sound design to create the ideal mood on the uncurtained, cozy stage. In tandem with their brilliant actors, they make “Intimate Exchanges” unforgettable theater.

Until July 1 (59 E. 59th St., between Park and Madison avenues, 212-279-4200).