Eagles perform in “History of the Eagles,” a new Showtime documentary. (Sam Jones/Showtime)

Years after they first called it quits, in 1980, members of the Eagles realized the emotional power of FM ubiquity, that their songs had fused permanently to a blue-jeans American experience. It was, as one of their early hits described, that “peaceful, easy feeling” of an era that has grown increasingly remote and exponentially nostalgic.

People “did things to [the music of] the Eagles,” frontman Glenn Frey observes in director Alison Ellwood’s tender and fascinating “History of the Eagles,” a two-part documentary beginning Friday night on Showtime.

People fell in love to Eagles music. They also broke up to it. They took spontaneous road trips to it, many of them through Winslow, Ariz., looking for the girl (my Lord) in that flatbed Ford. They brawled to it. They worked on their cars to it. They piloted space shuttles to it. It can’t help but make you think of ice chests and summertime, girls in tube tops and their shaggy-haired boyfriends. When listening to an Eagles song, “Everybody remembers a ’70s that they may or may not have had,” says J.D. Souther, a songwriter who collaborated with the band and watched it rise to the top.

The film beautifully depicts that “Almost Famous” feeling. Vivid footage from the band’s earliest days and chartered-jet apex is illuminated by hindsight, memory and some lingering resentments. “Later, when you look back at it, it looks like a finely crafted novel. But at the time it don’t,” says Joe Walsh, the guitarist who replaced original member Bernie Leadon in 1975 — just before the Eagles began recording their legendary “Hotel California” album.

Most of “History of the Eagles” is rich in detail and bemused reflection, perhaps because sobriety has worked wonders on some of the band members’ sense of recall. Frey, Walsh and Don Henley are wonderful storytellers. In only the film’s third hour, Saturday night’s conclusion, does the story take on extra bloat, as the Eagles reunite for an endless series of victory laps and arena shows through the late ’90s and 2000s in their Just for Men, relaxed-fit-denim era.

The first two hours, however, accomplish what all rockumentaries should, reveling in the basic miracle that opposite talents — Michigan-raised Frey and East Texan Henley — would meet and befriend each other, latch onto a certain sound, and set aside their differences to create a decade’s worth of hits.

The words “rare footage” are music to the ears of a certain sort of rock fan, and “History of the Eagles” has that to spare, including scenes from a 1977 concert in Washington. The film also nimbly recounts the ways the band contributed to (and capitalized on) the emergence of a Southern California country-rock sound 40 years ago. Frey recalls what it was like to live in a Los Angeles apartment above a young Jackson Browne, overhearing the singer-songwriter diligently trying to finish “Doctor My Eyes,” day after agonizing day. It taught Frey how hard it is to write a song — and made him realize that he would always need other musicians to help him do it.

Although rock stars complaining about the rigors of being on the road is nothing new, much of “History of the Eagles” is a more advanced rumination on the grueling labor that goes into sustaining a successful band. When they were inducted into the Rock and Roll Hall of Fame, in 1998, Henley told the audience that he felt the band should get the award “Not for being famous, but for doing the work.”

For one of its original members, bassist Randy Meisner, the end of that work came when he developed a case of stage fright over his ability to hit the highest notes in his Eagles hit “Take It to the Limit.” He just couldn’t face it anymore, so he left — an experience he reflects on with sadness. (He was replaced by the good-natured Timothy B. Schmit, who joined the band for the fraught recording of the “Long Run” album, released in 1979.)

“History of the Eagles” is also an interesting reminder of an old-fashioned music industry: the untold millions that could be made from actual record sales; the royalties picked clean by vultures; the troubles success could bring; the lawsuits filed against David Geffen (who graciously submits to an interview here); the fights with producers; the limitless cocaine; Walsh’s famously destroyed hotel rooms. All of it great fun and not quite the same in today’s pop-star realm.

After a 14-year cool-down (during which Frey and Henley separately achieved a string of MTV-era pop hits), the Eagles reunited in 1994 for a “Hell Freezes Over” tour and album. Frey and guitarist Don Felder found themselves at familiar odds, leading to one last ego clash, after which Felder left the band.

By the time the film enters its third hour, it seems like the Eagles should have more to tell us about growing old besides the platitudes they offer. There is little here about their personal lives or past relationships, and only fleeting glimpses of, and references to, spouses and children. The most haunting lyrics from “Hotel California” come to mind, about never being able to leave. Only now do you fully understand the relative comfort in staying.

History of the Eagles

Part 1 (two hours) airs Friday

at 8 p.m. on Showtime; Part 2
(70 minutes) airs Saturday at 8 p.m.