If an inside joke is so broad that pretty much anyone can grasp it instantly, does it really qualify as “inside”? Or, for that matter, as much of a joke?

Patrick Barlow’s strenuously silly parody of the 1935 Alfred Hitchcock spy thriller “The 39 Steps,” which has reached Broadway after considerable success in London, is designed to hurtle through music-hall gunfights, over Scottish moors, and atop speeding trains with such velocity that these sorts of questions should never spring to mind.

But despite Maria Aitken’s agreeably antic staging and the Herculean efforts of her four hardworking actors, Mr. Barlow pads his scene-by-scene homage with overly obvious references to other Hitchcock films, and sight gags that don’t go much of anywhere. Whenever the be-tweeded Richard Hannay (the droll Charles Edwards, a throwback to the pre-WWII era) conveys his mad flight from the police by running in place, the image seems unfortunately apt.

Produced at the tail end of Hitchcock’s London period, “The 39 Steps” served as a virtual template for many tropes that the director later drew upon repeatedly. Hannay, played by the effortlessly suave Robert Donat, is the prototypical innocent man on the run, lurching from one menacing scenario to the next à la Cary Grant in “North by Northwest” and Jimmy Stewart in “The Man Who Knew Too Much.” Madeleine Carroll, meanwhile, paved the way for such icy blondes as Tippi Hedren and Grace Kelly. And the title refers to a coveted set of British war data that drives virtually every scene without really being of the slightest interest to the audience — the very definition of what would become known as a “MacGuffin.”

This latter notion — the idea of being both central to the plot and utterly insubstantial — sits uncomfortably close to the heart of Mr. Barlow’s boisterous adaptation of the film (itself based on a John Buchan novel) and of Ms. Aitken’s frenzied direction. An awful lot happens in “The 39 Steps,” most of it conveyed through charmingly low-tech staging devices: The actors mime train voyages by jouncing in place and convey the windy Scottish countryside by fluttering their own overcoats wildly. The most expensive set element would appear to be the handcuffs that link Hannay and his semi-unwilling hostage, Pamela (Jennifer Ferrin), for most of the second act.

Much of the play’s appeal stems from the incongruous nature of this fairly picaresque yarn unspooling under such confining circumstances. But compared with Hitchcock’s later, more iconic films, “The 39 Steps” has relatively few puzzles to work out. Sure, there’s a train escape, a midnight chase across the moors, and a brief waterfall idyll, plus the obligatory Hitchcock cameo, but at least Hannay doesn’t need to contend with any Mt. Rushmore noses, murderous crop dusters, or crow-covered jungle gyms.

Actually, the crop dusters and a few (benign) crows show up anyway. In one of Mr. Barlow and Ms. Aitken’s many ostensibly clever notions, the action pauses several times for extraneous gags that even the most casual Hitchcock fan will spot from a mile away:

MARGARET: Quick! … Through the window!

HANNAY: Right.

MARGARET: Not that window!

HANNAY: Well, which window?

MARGARET: The rear window!

Even with these often awkward pit stops, Mr. Barlow and Ms. Aitken manage to fly through the entire film in scarcely more time than the original’s 86 minutes. This is a welcome change from the likes of “Spamalot” and the Disney musicals, which think nothing of adding an additional hour to their source material.

All the same, “The 39 Steps” represents a full night’s work for its four performers, who among them take on several dozen characters — a fact that also comes in for pointed, if predictably overstated, mockery near the end of the play. But with Mr. Edwards on full-time Hannay duty and with only a half-dozen or so female roles in the whole story for the appealing Ms. Ferrin, the vast majority of the quick-change artistry falls upon Arnie Burton and Cliff Saunders. (This being a British comedy, those two even get a crack at some of the female characters.) Messrs. Burton and Saunders throw their all into the lame gags as well as the funny ones, and their frantic maneuverings as they wriggle in and out of Peter McKintosh’s versatile costumes generate many of the evening’s laughs. If “actors are cattle,” as Hitchcock famously stated, Ms. Aitken has found herself some Grade-A prime beef.

Mic Pool’s sound and Kevin Adams’s lighting designs warrant mention as honorary co-stars; Mr. Pool’s ever-present sound effects and musical snippets (including a few recognizable strains from the Hitchcock oeuvre) play a crucial role in establishing mood and location, as do Mr. Adams’s razor-sharp juxtapositions and close-up-friendly shadows.

But while these four actors may be ready for their close-ups, their sketch-comedy shenanigans are only sporadically ready for prime time. The Hitchcock cameo is pretty funny, though.

Until March 23 (227 W. 42nd St., between Broadway and Eighth Avenue, 212-719-1300).