Consider how unusual it is for the exact breaking point of a big-time rock band to be chronicled on film.

The Beatles’ “Let It Be” showed a slow disintegration. For the Eagles, the end came abruptly at a political fundraiser in 1980. Don Felder didn’t want to be there. Glenn Frey didn’t like his attitude. Add years of simmering resentment and, as they performed, threats exchanged under the music. Fists didn’t fly, but by the time each stalked into separate limousines, the Eagles were toast for 14 years.

It’s one of the fascinating moments in “History of the Eagles,” a documentary that airs on Showtime Friday and Saturday. The film has two parts, just like the band, which has been together again since 1994.

Frey, 64, said it was time to get the story on film while the health and memories of everyone involved were intact. The Eagles courted filmmaker Alex Gibney, who won an Academy Award for his 2007 documentary on torture, “Taxi to the Dark Side,” after being underwhelmed by the work of some specialists in music documentaries.

Gibney expressed interest if he was free to tell a real story, not just an authorized one, and the Eagles agreed. He talked to each former member and associates like David Geffen, whose business relationship with the band ended badly.

Another key for Gibney was having enough footage to make the story come alive. Here he got lucky; although Frey and co-leader Don Henley were suspicious of outsiders during the height of the Eagles’ fame, they had the foresight to allow some filming, including extensive interview and concert footage from 1977, and that ill-fated 1980 benefit. Film was found of Frey and Henley playing in Linda Ronstadt’s backup band at Los Angeles’ Troubadour nightclub before the Eagles were born.

“Theirs is the classic rock ’n’ roll story – scruffy kids hook up in L.A., form a band and have enormous success and at the height of their success they break up,” Gibney said. “It’s a rock ’n’ roll fable.”

Frey hopes the film clears up misconceptions, primarily that the band’s time was dominated by squabbling. They worked hard and had a lot of fun, Frey said.

Oh, but they could fight with the best of them.

Those stories enliven the film: Bernie Leadon exiting after pouring a can of beer over Frey’s head; Randy Meisner leaving when he became reluctant to sing “Take It to the Limit,” his signature song; Felder ending his association with the reunion after getting a brutal business ultimatum from Frey.

Frey’s reasons for dissatisfaction with Felder are quite clear and although Felder is interviewed, his side of the story is murkier. The film’s most poignant moment comes when Felder breaks down and walks away from the camera when talking about it. “It just broke my heart,” he said.

Frey said there were never any serious problems between him and Henley.

“We just grew tired together,” he said. “That’s the way it played out. The Eagles became such a burden. I think Don and I just sort of succumbed to the weight that we felt after ‘Hotel California’ went through the roof. You know, it could have ended there. Instead for us, we were able to, as Don said, have a second act.”

Since the Eagles famously said they wouldn’t re-form “until hell freezes over,” their reunion was cheekily called the “Hell Freezes Over Tour.”

The meat of the Eagles’ story is in the documentary’s first part, but the band didn’t want their “second act” shortchanged, Gibney said.

The Eagles are less a creative force now than a business colossus that tours all around the world. The most interesting segment in the second part is the journey of Joe Walsh, the former court jester who learned hotel room trashing from that art’s Picasso, Keith Moon. For his survival, as a person and an Eagle, Walsh needed to clean himself up and has succeeded.

After devoting much of their attention to the documentary the past year or so, the Eagles are mulling the future, perhaps incorporating some of the film’s visual elements into a live show that revisits some songs that haven’t gotten much attention lately, Frey said.

“What happened when we got back together is we realized that the Eagles is this mothership that makes everybody’s life better,” he said. “We all understand what a unique position we’re in, individually and collectively, and it’s nice to be able to keep the Eagles going. We always say that as long as we’re able to go out onstage physically and perform at a high level, we’ll continue to perform.

“Obviously it’s not going to last forever,” he said. “But I think we still have a few more miles.”