When a comedian is considered historically important, it’s often code for “no longer funny.” Lenny Bruce broke more ground than any comic, but his old routines now inspire more respect than laughs. So I approached the two-hour film of the farewell performance of the English satirical revue “Beyond the Fringe,” playing at the Museum of Television and Radio through March 31, with some trepidation. Has any comedy show been more historically important?

“Beyond the Fringe” – written and performed by four smarty-pants Oxbridge students with limitless futures, Dudley Moore, Jonathan Miller, Alan Bennett, and Peter Cook – kicked off the British satire boom of the 1960s. This included television shows (“That Was the Week that Was,” magazines (Private Eye), a nightclub (The Establishment, founded by Mr. Cook), and one seminal comedy troupe, Monty Python. The members of Python – another gang of Oxbridge cutups – credited “Beyond the Fringe” as their major influence. One could also make the argument that Jon Stewart, Saturday Night Live and The Onion are all the offspring of Beyond the Fringe.

But forget all that for a moment. There is a better reason to run over to the Museum of Television and Radio: “Beyond the Fringe” is very, very funny. Not funny for something that was done four decades ago, but belly-laugh hilarious right now.

Since the group’s targets were so large (the royal family, organized religion, Shakespeare, pompous philosophers), their topical references won’t be lost on many audiences. In fact, “Beyond the Fringe” feels less dated than a month-old episode of Saturday Night Live, whose targets have become so small (Al Sharpton, shows on Bravo, Nicole Richie) that hardly anyone really cares.

Performing in black suits and skinny ties, the four clean-cut young men look like they’re ready for their class picture. But don’t be fooled. These baby-faced jokers practice bareknuckle comedy; their potshots hurt.

The show opens with the group talking about America in plumy, pompous British accents. “Isn’t there a lot of poverty in America?” Moore asks, to which Mr. Cook, who wrote most of the material, responds, “Yes, but it’s concentrated in the slum areas, which is very convenient.”

“Beyond the Fringe” may not have been as inspiredly silly as Monty Python, but it attacked its targets with more force. Its most controversial sketch, “The Aftermyth of War,” sent up the earnest World War II documentaries that portrayed the English as stoic fighters who defeated the Nazis just in time for tea. One critic called it “vaguely indecent for 20-year-olds to be making fun of Battle of Britain pilots.”

But “Beyond the Fringe” was as serious about silliness as it was about politics. The show is packed full of dense punnery and tongue-twisting wordplay. In a literary critic’s monologue about T.E. Lawrence, Mr. Bennett says, “There are some who said there was something feminine about his make-up. But there is nothing essentially feminine about makeup. And he was always very discreet.”

Python fans will find direct echoes of its style in sketches such as the one about the one-legged actor auditioning to play Tarzan. Dudley Moore hops around the stage in a variety of absurd movements that bring to mind the Ministry of Silly Walks. The director, played by the eternally deadpan Mr. Cook, finally tells this unwavering optimist that nontraditional casting has its limits. “It is in the leg division that you are deficient,” he said. “You are deficient to the tune of one.”

The theme that dominates most of the skits is that the people in charge don’t know what they’re talking about, but they fool everyone by using portentous-sounding rhetoric. The priest is a fool. The logic games of analytic philosophers are a waste of time. And in an hilarious send-up of Shakespeare, Mr. Miller finishes off a soliloquy of empty declamations with this couplet: “I most royally shall now to bed, / To sleep off all the nonsense I’ve just said.”

“Beyond the Fringe” was trailblazing in how brazenly it addressed subjects of race, class, and sexuality. Precisely for that reason, some of their jokes don’t age terribly well. It’s hard to imagine that the following exchange would past muster today: “I understand that Negroes are sweeping the nation.” “Yes, it’s the only job they could get.”

“Beyond the Fringe,” which premiered in the Edinburgh Fringe Festival in 1961, had a relatively short stint. It moved to the West End and eventually to Broadway’s Golden Theatre, where it played its final performance in 1964. But the members of the group all went on to impressive careers.

Of the group, Cook, who passed away in 1995, had the least illustrious post-Fringe career. Moore, who died in 2002, briefly became a Hollywood star with films like “Arthur” and “Ten.” Mr. Miller is a respected stage director. Alan Bennett has become one of England’s greatest playwrights; his most recent play, “The History Boys,” was a hit at the National Theatre and will likely transfer to the States.

“Beyond the Fringe’s” brief shelf life makes the current screenings even more of a must-see. Unlike Python, “Beyond the Fringe” was not rediscovered by successive generations in late-night movies and television repeats. “Spamalot” is already packing in thousands of fans every week; on a recent weekday at the Museum of Television and Radio, only a small handful of fans showed up to see “Beyond the Fringe.”

That shouldn’t surprise anyone. In American culture, and especially Broadway, the copy is usually more popular than the real thing.

Until March 31 (25 W. 52nd Street, at Fifth Avenue, 212-621-6800).