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T'S no wonder progressive rock was nearly laughed out of business when punk rock came along. With its album-length suites and cosmic philosophizing, its quasi-classical pomp and showy instrumental interludes, prog rock was long-winded, pretentious, cerebral, fastidiously technical and decidedly self-indulgent - all of which suddenly became no-nos as punk attacked all the ways rock had grown hifalutin and out of touch in the 1970's. Prog had been nerdy all along, the province of musicians and fans who could get all excited about a meter change or a dissonant guitar line. And punk destroyed any hopes that prog might have harbored of gaining cachet to match its elevated ambitions.

But prog is now resurfacing, not only among the diehards who never let go of it - bands like Rush and Dream Theater, labels like Cuneiform Records - but also for younger musicians and fans. Radiohead's most recent albums brought the grandeur of progressive rock back into the Top 10, while the college circuit supports bands as diversely proggy as Coheed and Cambria, which sounds like outtakes from old Rush albums, and the stately, largely instrumental bands Mogwai and Sigur Ros. This week the Mars Volta, a band from El Paso that is prog-rock despite its members' protestations, releases its second more-or-less concept album, "Frances the Mute" (Gold Standard Laboratories/Strummer/Universal).

Until recently, neither fans nor mockers admitted that progressive rock could also provide some of the same thrills - speed, whipsaw changes, sheer pummeling impact - as punk. That's why many of prog's musical twists migrated elsewhere in the 1980's and 1990's: the odd meters to hardcore and thrash metal, the dissonance to primitivist art rock, the convoluted song structures to indie rock and its proud subset of math rock.

Prog may have been hopelessly uncool, but it was nothing if not alternative. Despite its brainy reputation, at its core it was a rebellion against ordinary pop. By any objective reckoning, it was also deeply demented. Who, after all, would labor over a suite in 13/4 time pondering the meaning of free will when the way to gigs and hits was with catchy love songs?

Dementia reigns, to good effect, in the Mars Volta. The band was formed in 2001 by Omar Rodriguez-Lopez and Cedric Bixler Zavala, two former members of At the Drive-In, a college-circuit emo band that fissioned on the verge of wider recognition. (Three other members formed Sparta.) Its first full-length album, "De-Loused in the Comatorium" in 2003, was conceived as the visionary deathbed fantasies of a comatose man. "Frances the Mute" grew out of a diary, found by a band member, of an adopted man seeking his biological parents, and its five extended, multipart songs are named after characters from the diary.

That's according to the band's Web site. True to prog-rock precedent, the lyrics are both copious and hermetic. The Mars Volta's singer and lyricist, Mr. Bixler Zavala, spews streams of consciousness in English and Spanish. They are not for the squeamish: "Behind the snail secretion leaves a dry heave that absorbs a limbless procreation." It would take more than a decoder ring to decipher a storyline on "Frances the Mute," though there are glimmers: "I won't forget who I'm looking for/Oh mother help me," the singer moans in "L'Via L'Viaquez."

Ancestry matters in the music on "Frances the Mute" - both the band's musical precursors and the band members' mixture of Anglo and Hispanic roots. But as with the adopted man in the songs, inheritance means less than its unkempt present-day transformations. The 1970's legacy defines the opening moments of the album, with 12-string guitar and an echoey high voice singing dreamily about "the ocean floor," proving that the Mars Volta has been listening to Led Zeppelin and Yes. Throughout the album, Mr. Bixler Zavala's high tenor veers between Robert Plant's blue wails and Jon Anderson's eunuch harmonies, and the bottom-scraping crunch of Juan Alderete de la Peña's bass lines also echoes Yes. But unlike some latter-day prog-rock the Mars Volta won't be mistaken for anything from the 20th century.

The closest it comes is in the album's low point (and single), "The Widow," which may be trying to placate radio programmers by offering three mintes of chest-heaving Led Zeppelin homage. But on the album, the band finishes the track with a tangent: an additional two minutes of woozy, abstract keyboards.

More often, the music combines the kitchen-sink inclusiveness of psychedelia with the swerves and jolts of the hip-hop era, to approach the ravenous eclecticism of Latin alternative rock. The Mars Volta embraces musicianly complexities, showing off virtuosity by revving the songs up to frenetic tempos. But it rejects the compulsive neatness that classically trained musicians brought to prog-rock in the 1970's.

A big part of the difference is that punk and hip-hop have trained rock to look for the vulgar before the cosmic. The Mars Volta's songs are expansive, but they're not ethereal. Technical feats like the ones the Mars Volta pulls off in every song can make music seem like a purer, cleaner realm, an escape from imperfect reality. But not in these songs. As the band's producer, Mr. Rodriguez-Lopez keeps the songs raggedly and aggressively concrete. He uses guitar distortion, horn sections, sound effects and what sounds like the manipulation of old-fashioned recording tape to match the music to the near-toxic atmosphere of the lyrics.

Clashes, mutations and sudden leaps fill the songs, which can linger for long minutes over an (odd-meter) vamp and one of Mr. Omar-Rodriguez's jabbing guitar solos or switch instantly between disparate styles. "L'Via L'Viaquez" moves between two characters, two languages, two voices (a clarion, paranoid wail in Spanish and a furtive whisper in English), and two musical idioms: bruising, accelerating funk behind the Spanish, which warns of death threats and vengeance, and a slow, deliberate Latin vamp behind the English, urging, "Don't be afraid." To scramble expectations further, the Latin stretches feature Larry Harlow, a pianist who was an essential member of the 1970's salsa supergroup the Fania All-Stars.

That kind of willfulness fills the album. "Miranda That Ghost Just Isn't Holy Anymore" starts with a full minute of chirping birds (or crickets) before gradually drifting into a mournful waltz with hints of both early King Crimson and mariachi horns.

And lest anyone doubt the band's affinity for the old-fashioned epic, the longest song on "Frances the Mute" is also the album's tour de force. For most of its 32 minutes, "Cassandra Geminni" hurtles ahead on a tightly wound, breakneck guitar riff; its first section is called "Tarantism," named for the uncontrollable urge to dance supposedly caused by a tarantula's bite. Mr. Bixler Zavala sings about birth, darkness and destruction; guitars and bass work in contrapuntal patterns, strings and horns pile into the mix, the song dissolves into free jazz and reappears. It's wildly, glorious excessive, indulging the prog-rock impulses that are simply too ecstatic for rock to leave behind.