"While the band did break up in 1980, our music continued without us," wrote Glenn Frey in 2000. "It was becoming increasingly apparent to me that, no matter where I went or what I did, for the rest of my life I would always be an Eagle."
Glenn Frey, who has died aged 67, was justifiably proud of his band's achievements. Their meticulous harmonies and relaxed country-rock sound dominated airwaves and cassette decks in the 1970s, with global album sales in excess of 150 million.
Don Henley called Frey "the glue" of the band - a business-minded taskmaster who steered them towards commercial success.
"He's a big sports fan, so he applied coaching principles to running this band," said the singer. "He recognises people's strengths and gets them to do what they do best."
The band's manager, Irving Azoff, said: "Early on, he was running around with a T-shirt that said, 'Song Power'.
"[He] was saying the Eagles were a team and not everybody can be the running back or the quarterback. He was the quarterback."
Frey's lofty ambitions were fulfilled by Hotel California, The Eagles' fifth album. Released in 1976, it sold 16 million copies in the US and double that figure worldwide.
While they had been successful before - a greatest hits album collection released earlier the same year had become their first number one - Hotel California was "the zenith of The Eagles", said Frey in 1992, "in that what we had to say came together with our learning of how to make records".
It sealed the band's reputation. It also sealed their fate.
The title track remains their most famous recording, a long and intricate rock ballad whose duelling guitar coda has been named the best solo of all time.
It is ostensibly about a luxury hotel visit that crosses over to the dark side - but it is really an allegory about the hedonistic lifestyle the musicians enjoyed in the 1970s.
Or at least, that's the most popular interpretation. The song was also rumoured to be about heroin addiction, cannibalism or devil worship (the album cover allegedly shows Anton LaVey, leader of the Church of Satan).
"Everybody wants to know what that song was about, and we don't know," Frey said in a BBC interview eight years ago.
A decade earlier, he was more forthcoming, telling NBC's Bob Costas that he and Henley "wanted to write a song that was sort of like an episode of the Twilight Zone".
"All of our songs were cinematic, but we wanted to open up with [a montage]," he said.
"It was just one shot to the next - a picture of a guy on the highway, a picture of the hotel, the guy walks in, the door opens, strange people.
"We take this guy and make him like a character in The Magus, where every time he walks through a door, there's a new version of reality.
"We decided to create something strange, just to see if we could do it. And then a lot was read into it - a lot more than probably exists.
"I think we achieved perfect ambiguity."
While Henley and Frey wrote the lyrics, guitarist Don Felder composed the bulk of the music, initially recording the song's 12‑string riff in his four‑track home studio.
When he first played it to the band, they perceived it as "a bizarre mix of musical influences" and the song's working title became Mexican Reggae.
Recording began in Los Angeles, but the first version of the song was in the wrong key for Henley's raspy vocals.
"He sounded like Barry Gibb in this high voice," said Felder, who transposed the song from E minor to B minor "which is not a particularly guitar-friendly key, but it was perfect for his voice".
A second recording turned out to be too fast, so the band started again in Miami, fine-tuning the instrumentation and the lyrics in the process.
"When we recorded it the third time, that was the charm," producer Bill Szymczyk told Sound on Sound magazine.
The band recorded several takes, then spliced together the best bits to create the version we know today.
"At this stage in their career, The Eagles were pursuing perfection," said Szymczyk, "and in the process of editing I'd hear, 'Well, see if you can do that, Coach,' which was my nickname back then.
"This might refer to replacing one drum fill with another fill that was a little better, so there'd be an edit at the front and an edit at the end. That's the kind of perfection we were dealing with."
Once the basic track had been constructed, it took two days to record the closing guitar solos, with Felder and Joe Walsh trading riffs side-by-side in the control room.
Felder had initially assumed they would improvise this section - but Henley and Frey had other ideas.
"Joe and I started jamming, and Don said, 'No, no, stop. It's not right,'" Felder said in an interview with Music Radar. "I said, 'What do you mean it's not right?' And he said, 'You've got to play it just like the demo.'
"Only problem was, I did that demo a year earlier; I couldn't even remember what was on it. So we had to call my housekeeper in Malibu, who took the cassette, put it in a [ghetto]blaster and played it with the phone held up to the blaster.
"We recorded it, and I had to sit in Miami and play exactly what was on the demo."
The perfectionism paid off. Hotel California is the band's most enduring song, still played more than 200 times a month on UK radio, and covered by artists as diverse as The Gipsy Kings, The Killers and Frank Ocean.
When a US spy plane made an emergency landing in China in 2001, the crew members were asked to recite the lyrics to prove their nationality. Apparently, their Chinese captors considered that "the song symbolised America".
Henley would have disagreed. "We were all middle-class kids from the Midwest," he told Rolling Stone. "Hotel California was our interpretation of the high life in Los Angeles." In 1995, he referred to the record as being about a "loss of innocence".
The album, which also contained the singles New Kid In Town and Life In The Fast Lane, "was the best work we did together," Frey said in 1992.
"We were bristling with confidence. We weren't afraid to step out and take chances. And we had a very, very prolific couple of guitar players," he said.
Critics may have accused the Eagles of being too slick and polished, but the band had the perfect riposte - 16 platinum discs.
"Critics lose their leverage all of a sudden when something gets mass acceptance," said Frey. "They're no longer arbiters of taste."
Still, the accusations stung. Reviewers who poured scorn on the band were added to a "punch on sight" list.
But success had a downside. The band found themselves creatively confounded, obsessing for three years over follow-up album The Long Run.
"It had stopped being fun," Frey later told the Independent. "We no longer trusted each other's instincts, so there was considerable disagreement. Plus, both Henley and I had developed drug habits, which didn't help matters.
"Going to the studio was like going to school - I simply didn't want to go. But most importantly, during the making of The Long Run, Henley and I found out that lyrics are not a replenishable source.
"We, Don in particular, said a mouthful on Hotel California, and a big part of the problem was, 'What do we talk about now?'
"Towards the end, we just wanted to get the record finished and released. It is a very polished album, as well it should be after all that, and has some excellent moments, but none of us wanted to go through that again."
Things came to a head as the band wound up their 1980 tour with a benefit show in support of California senator Alan Cranston.
According to Frey's account, Mr Cranston came backstage before the concert to thank the band for their efforts, but Felder responded with a less-than-enthusiastic: "You're welcome, Senator… I guess."
It led to a huge backstage row, with beer bottles smashed against the wall. "I felt Don Felder insulted Senator Cranston under his breath, and I confronted him with it," said Frey.
"So now we're on stage, and Felder looks back at me and says, 'Only three more songs till I kick your ass, pal.'
"We're out there singing Best of My Love, but inside both of us are thinking, 'As soon as this is over, I'm going to kill him.'
"That was when I knew I had to get out."
Fourteen years elapsed before the bandmates made amends and recorded the aptly named Hell Freezes Over album.
"Any worthwhile relationship has to survive extremes." Frey said on the first of many lucrative world tours.
The reunion also produced an album of new material - Long Road Out Of Eden (their only UK number one) - and won the band a new generation of fans.
"It's a lot of fun to see," said Frey in 2001. "We're like the Energizer bunny in that commercial. We just keep going and going and going…"