In spring 1975, DJs across the country received unmarked records from the label RSO. It was a new single from a mystery band. When they dropped the needle on "Jive Talkin'," the DJs were convinced: this was a hit, and they had to play it. But who were the musicians? Were they white or black? American? European? Australian?

When they heard the answer, DJs were shocked. It was a band from the oldies circuit, best known for a string of schmaltzy hits in the late 1960s. As recently as 1974, they were still touring with an orchestra, strung out and broke and brawling backstage — even though they were brothers. It was the brothers Gibb, the Bee Gees.

Today, when someone says "Bee Gees," the average listener pictures the three brothers in their iconic white suits, intentionally selected to match the one John Travolta wore in the movie Saturday Night Fever. In the disco era, though, the Bee Gees were unlikely comeback stars. Simon Spence's new book Staying Alive: The Disco Inferno of the Bee Gees tells the story of how the brothers reinvented themselves as dance-floor heartthrobs.

The brothers were prodigies, first performing together as a family band when they were still young children in Australia — having relocated from the Isle of Man, where Barry, Maurice, and Robin were all born. Their father Hugh was a taskmaster not unlike Joe Jackson, a fact that perhaps helped to forge a later bond of friendship between Barry Gibb and Michael Jackson.

They moved to the U.K. in 1967, in part so that Barry could dodge the draft and avoid being sent to Vietnam with the Australian military. They signed with producer Robert Stigwood, a veteran promoter who had just acquired the Beatles' management company and was looking for his next set of stars. The Bee Gees were still unformed, but Stigwood recognized the enormous potential of a brother band who had written such impressive songs while still only teenagers.

With Stigwood's guidance, the Bee Gees quickly racked up a major string of hits. "New York City Mining Disaster 1941," "To Love Somebody," "Massachusetts," "I Gotta Get a Message to You," and "Words" were among their big singles on both sides of the Atlantic, all of them eminently radio-friendly...and if they weren't as cool as the Beatles, they were cool enough. They were partying with Rod Stewart and David Bowie, buying John Lennon's cast-off cars, and, in Maurice's case, marrying young star Lulu ("To Sir With Love").

By the mid-1970s, though, the group's star had fallen. They were struggling to remain relevant, and Maurice was spiraling into addiction as his marriage ended. Stigwood's attention was on the successful shows he was producing, including Jesus Christ Superstar, Hair, and the Who's film Tommy. They were still dressing in dandyish '60s-style outfits, and they were depressed about it.

Still, they decided to give it one more go. Though solo careers beckoned, they realized they were stronger as a group. At Eric Clapton's suggestion, they decamped to Florida, where Eric Clapton had revived his career with an album named after the address of the Miami studio where it was recorded, 461 Ocean Boulevard.

The Bee Gees hunkered down in the same studio, with respected soul producer Arif Mardin and engineer Karl Richardson — a disco-loving hippie who pointed Barry towards the pulsing sound of the city. Barry started to think about using his pristine falsetto, a voice he'd previously been hesitant to employ since it didn't sound very masculine.

The breakthrough came as the band drove across the four-mile Julia Tuttle Causeway bridge in Miami. Over the rhythm of the wheels on the the bridge, the brothers wrote a melody that they presented to Mardin as "Drive Talkin'." When synth player Blue Weaver added a hook inspired by Stevie Wonder's early '70s classics, the Bee Gees knew they'd found their winning formula.

Not only was "Jive Talkin'" a hit, it crossed over to the R&B charts — and the album Main Course was released without a photo of the band on the cover in hopes that their newfound African-American audience wouldn't realize the Bee Gees were white.

"Jive Talkin'" and "You Should Be Dancing" were hits without the help of the movies, but Stigwood had the inspiration to bring the band's new sound together with a movie he was producing, a gritty street drama inspired by the New York magazine feature "Tribal Rites of the New Saturday Night." Travolta would star, although he was nervous because he didn't think of himself as much of a dancer. Could director John Badham convincingly mix exuberant nightclub scenes with realistic urban drama?

The production was already three weeks in when the Bee Gees' new tracks arrived, including the sexy ballad "How Deep Is Your Love" and a new disco song called "Stayin' Alive" — with a long breakdown bridge, added at Badham's behest. Suddenly, everyone knew: the film was going to work. It was really going to work.

The dance scenes were filmed at 2001 Odyssey, a Brooklyn club that was one of the locations described in the New York article. The filmmakers built a fancy new floor, and cast the club's regulars as extras. The result was an effortless sense of authenticity, and Travolta wisely insisted that his scenes be recut when he saw that Badham didn't plan to show his feet.

The Bee Gees, already back in a big way, became superstars. The soundtrack album spent almost six straight months at number one, and discomania ruled the world. Even the kids' album Sesame Street Fever went gold.

The Bee Gees had a couple more years of disco success, but the writing was on the wall. When the Knack's "My Sharona" hit number one in 1979, it was seen as heralding a "new wave" of post-disco, post-punk pop music. The Chicago White Sox's infamous "disco demolition" game that same year — when fans were offered reduced admission if they brought a disco record to destroy, and the resulting melee led to a near-riot — pretty much sealed the casket on the disco era.

The Bee Gees carried on, despite continued personal problems including the addiction-linked death of their younger brother Andy in 1988. They remained a chart force throughout the '80s, hitting the top ten in 1989 with "One." In 1997 they were inducted into the Rock and Roll Hall of Fame, where their official biography describes them as "'70s icons."

As the Saturday Night Fever soundtrack celebrates its 40th anniversary, Spence's book offers a welcome portal back to that era of chest hair and chains, when the dance floors were on fire and when all the world, it seemed, was dancing to the Bee Gees' beat.