Regimes and revolutions come and go, but the Plastic People of the Universe are forever.

Nearly 40 years after its members first switched on their amplifiers in the chilly aftermath of the Soviet invasion that ended the Prague Spring of 1968, the band is back on the road: grizzled, defiant, and rudely effusive with its lurching rhythms, untempered skronk, and philosophical jokes that seem partially lost in translation.

Vratislav Brabenec, the group’s 63-year-old saxophonist, was introducing one of the opening numbers in Czech before a crowded audience of about 150 fans at the Cutting Room in Chelsea on Saturday night — a rare New York appearance by the Plastic People, who will also perform tonight at the Knitting Factory.

Many in attendance were there in conjunction with a symposium at Columbia University, where former Czechoslovakian and Czech Republic president Václav Havel recently began a seven-week residency. So perhaps a translation of Mr. Brabenec’s comments was not entirely necessary. But Eva Turnova, the young, red-haired bass player who joined the group a few years ago, offered hers anyway: “What it means is, we kill a pig and then we eat it in one day.”

Turn that barnyard analogy to any purpose you please, but it does speak to a certain unvarnished folk wisdom. The Plastic People epitomize a whole-hog aesthetic that regards any element as useful, without much concern for tidy trimmings. Their songs have a tilted, out-of-focus feel, thanks to those old village dance rhythms and what can only be described as a curiously lustful melancholia — given the odd collusion of Jifií Kabe’s bittersweet violin and Mr. Brabenec’s frequently squealing saxophone.

The band, which took its name from a Frank Zappa tune, stuck to its classic material for most of the 90-minute show, evoking the American subculture hero’s fuzz-haired eclecticism in songs that, as Ms. Turnova offered later, were not so much explicitly political as merely oddball and artinflected. The Plastic People became revolutionary martyrs in the 1970s because the mere notion of American-influenced rock musicians creating a public spectacle was an inherent threat to Soviet dominance. Or, as the Talking Heads would put it back when these rowdy Czech hippies were still consigned to a kind of public exile: “Electric guitar is a crime against the state.”

At the Cutting Room, the band was mostly absent that weapon. The lead guitarist was sick, and only appeared for a song or two. And because they often sang lyrics as a chorus, the musicians sounded less like subversive rock legends than a wandering gypsy freejazz punk outfit that had missed its bus at the Port Authority and was gigging for free beer and cigarettes. And gloriously so.

There has never been anything trendy or even terribly commercial about the band’s choices. Czech communist rule forced the musicians off the public stage in 1970, and a notorious, aborted 1974 performance in the village of Budovice that attracted thousands of fans ended in police violence and arrests. During the late 1970s, when English punk-rock acts like the Clash preached revolutionary rhetoric that became a gesture of style, two of the Plastic People were living with the consequences of physically rejecting political oppression of free speech. They were in jail, serving out eightmonth terms for a 1976 conviction of public disturbance. That is, they were arrested for rocking.

Despite the arrest and the subsequent governmental ban on performances, the band thrived underground, inspiring the Charter 77 movement that anticipated the Velvet Revolution of 1989, which swept their friend and supporter Mr. Havel into power as the Soviet Union crumbled.

All these years later, the group’s current tour makes it seem as if it has popped out of a time capsule. Indeed, given their crazy-quilt history, the older musicians might feel as though they are now reaping the rewards of their struggle. Tom Stoppard’s new play “Rock ‘n’ Roll,” now at the Royal Court Theatre in London, celebrates the band’s insurgent saga (as did a 2001 documentary about the band). And while the death in 2001 of its founder, Milan Hlavsa, left the outfit with only three original members, its current multi-generational lineup appears fully invigorated.

Astonishingly, on Saturday the music shifted between comic a capella and fluid improvisational jamming in the space of a single song, implying that the band might be equally at home playing the neo-hippie Bonnaroo Festival as it would be at the late, lamented CBGB.

As Mr. Brabenec noted from the stage, the group has been traveling a lot, recently headlining a concert in St. Petersburg. “They were very nice,” he said later, puffing on a Chesterfield outside the venue, where fans young and old hovered for bits of conversation and autographs. “Russian people are very nice people.” Then he added, with a touch of commentary: “Russians and Americans are almost the same people. They know anything about everything.”

Mr. Brabanec looks quite a bit like one of the Fugs — the irreverent leftie rabble-rousers Tuli Kupferberg and Ed Sanders — who were one of the big influences on the Plastic People, and who have joined the group onstage during previous New York appearances. He was happy to be back in town, in part through the agency of Mr. Havel, for whom he offered affection but also criticism. The Velvet Revolution was, maybe, “too much velvet,” he said, suggesting that the hardliners of the old regime got treated too softly when they should have been kicked out of their apartments. But he had little else to complain about.

“I’m still playing,” he told someone in Czech as he finished his cigarette. “Still drinking. Still f—ing.”