In British parlance, communicating doors connect adjoining hotel rooms. In Alan Ayckbourn’s play “Communicating Doors,” they are a portal to another time.

Part “Back to the Future” and part “Psycho,” Ayckbourn’s time traveling sci-fi comedy thriller has plot complexities galore, but Cygnet Theatre’s current production is lively, light summer fare that entertains with a fine ensemble.

A prolific and popular English playwright, at 72, Ayckbourn has penned 70 full-length plays. “Doors” premiered in 1994 at the Stephen Joseph Theatre in Scarborough, where Ayckbourn has been artistic director nearly consecutively since 1972. (He plans to step down next year.)

The opening scene of “Doors” takes place in London in 2027, where “specialist sexual consultant” Poopay is ostensibly hired to give a dying man one last hurrah. But filthy rich businessman Reece isn’t interested in sex; he actually wants the rather mousy dominatrix to convey to lawyers a confession of past misdeeds that include the murders of his two wives. But Reece’s business partner Julian – implicated in the confession letter – discovers the plot and the document and, naturally, has to off the girl, who knows too much.

That’s when the fleeing Poopay discovers the communicating door, which leads her to an identical room, 20 years in the past.

Back in 2007, our unfortunately named heroine meets Reece’s second wife Ruella, on the very night that Julian is slated to murder her. After some initial confusion, the two women figure out that the communicating door is some kind of portal linking them, but that it only unlocks the past.

Ruella discovers that she, too, can travel back 20 years, and lands in the same room in 1987, intruding on the honeymoon of Reece and wife No. 1. Ruella and Poopay hatch a plan to convince sweet but dim-witted Jessica that her life is in danger – albeit seven years henceforth – while also avoiding villainous Julian versions 2007 and 2027.

All the while, a smug, self-serving hotel detective tries to eject the time-travelers from the posh hotel, in both 1987 and 2007.

Sound confusing?

The plot only gets more twisted (with a few surprises in store), but it all makes sense thanks to Ayckbourn’s seemingly easy-breezy writing and Esther Emery’s surefire, brisk direction. Add some effective something-weird-is-afoot lighting by Eric Lotze, George Ye’s noir-ish music to murder to, and a revolving door in Nick Fouch’s cleverly designed hotel room set, and you’ve got a moody, handsome sci-fi mystery that keeps you guessing – and laughing.

The ensemble deflty handles the humor, a mix of wit, one-liners and slapstick. Jessica John, in costume designer Shulamit Nelson-Spilkin’s strappy stilettos and dungeon-wear leather, is the proverbial hooker with a heart of gold. She brings sincerity and warmth, and a good dose of humor, to the central role. Sandy Campbell also turns in an excellent performance as the no-nonsense, level-headed and courageous Ruella.

Manny Fernandes is perfectly menacing and creepy as Julian, and Craig Huisenga turns up the humor as the obsequious hotel detective. Tim West plays the affectionate septuagenarian most believably, but isn’t feeble enough as the sickly, aging Reece. Brenda Dodge is likeable as ditzy Jessica.

Conceptually, time travel is fun, but it always comes with inherent problems, i.e., if I go back in time and kill my grandfather, will I still be able to post my review on deadline in a parallel world, or will I unravel the very fabric of the space-time continuum and destroy the universe?

The point of the play, of course, is not to tease out the complexities of the concept, but to suggest that we all have the power to change the future by changing the present. Though the mechanism of time travel is never fully explained, it hardly matters. This production of “Doors” sweeps you up in its conceit and you’ll willingly play along.