guitarist Lindsey Buckingham and singer are joining forces for their first duet album.
The record, out Friday, is called "Lindsey Buckingham, Christine McVie."
Fleetwood Mac's 1970s hit "Don't Stop" from the album "Rumours" topped the charts for 31 straight weeks, but the band has always been known as a bit of a musical soap opera, reports CBS News' Anthony Mason.
McVie was married to bassist John McVie, and Buckingham lived with Stevie Nicks.
Both couples broke up, but somehow the band survived. Now, for the first time, Buckingham and McVie have teamed up musically.
"There's been a lot of drama among members of Fleetwood Mac," Mason said.
"Oh, you could say that," Buckingham said.
But Buckingham and McVie have never had drama between themselves.
"Not yet," Buckingham joked. The two began working on new songs together when she rejoined Fleetwood Mac after a long absence in 2014. Bandmates John McVie and Mick Fleetwood provide much of the rhythm section on Buckingham-McVie's debut duet album, which makes it an almost-Fleetwood Mac record. Everybody's on the album except Nicks, which had some people wondering if it started as a Fleetwood Mac album.
"No, it didn't really. There was no idea of saying, 'Oh we're trying to make a Fleetwood Mac album.' It was just, 'Let's get together and have some fun with this.' But as I said, it only took about a week for us to start to get a little territorial about it maybe being a duet album," Buckingham said.
Last month, they took over Sound Stage 22 on the Sony lot in Los Angeles to begin rehearsing for a summer tour.
McVie has been singing harmonies with Buckingham since he first joined Fleetwood Mac back in 1975 with his then-girlfriend Nicks.
"It was with Stevie and John, and it was a little studio somewhere," McVie said of the first time she and Buckingham sang together. "I was playing 'Say You Love Me.' And you and Stevie chirped in with fantastic background vocals. And we just all sat, I mean I sat there with goosebumps. I could not believe it."
They'd form the classic lineup of Fleetwood Mac. Their first album together went to number one. Their second, "Rumours," would sell more than 40 million copies.
But in 1998, tired of the travel and the feuding, McVie quit the band and moved to the English countryside, where she'd stay for 16 years.
"And it was OK for a few years, and then I just became quite isolated really," McVie said.
McVie did do a solo album during that time.
"How could I forget? In my garage, we call it 'the dirge' album. Cause I was in a dark space then," she said.
"Did you decide that you're not really a solo artist after all?" Mason asked.
"I know I'm not," she said. "I'm not."
McVie took her first tentative steps back into Fleetwood Mac in 2013, when Fleetwood invited her to join them for one gig at London's 02 Arena, a reunion captured on fans' cellphone video.
"He said, 'Why don't you just come on and do "Don't Stop" with us?' So that's, that's in the end what I did," she said. "And looking around at these other four individuals - it was just a mind-blowing experience."
Right away, she knew she wanted to go back.
"There is nothing like this extended family that is Fleetwood Mac. And I think you have to say, for all the perceived and real dysfunction that there has been, underneath that, there is and always has been a great deal of love. And that keeps pulling us back together," Buckingham said.
The Buckingham-McVie tour opens in Atlanta June 21 and runs through July.
Watch "CBS This Morning: Saturday" for the duo's Saturday Sessions performance and for more of Mason's interview.