Abba receive Hall of Fame honourBreaking News
Abba's Benny Andersson and Anni-Frid Lyngstad accepted their trophies, but Bjorn Ulvaeus and Agnetha Faltskog did not attend the ceremony in New York.
Andersson said: "I speak for all of us, we are deeply, deeply honoured."
He added that the band, who had hits with Dancing Queen and Waterloo, would never perform together again.
'Rebellious and restless'
After winning the Eurovision song contest in 1974, Abba went on to release a string of hits, including Knowing Me, Knowing You and Super Trouper.
During the awards ceremony, Andersson accompanied Faith Hill on the piano as the country star sang one of their songs, The Winner Takes It All.
Lyngstad, who was once married to Andersson, said: "I am truly very touched by what once started as partnerships a long time ago - and that this has brought us here tonight."
Genesis were inducted by Trey Anastasio of Phish, whose band paid tribute to both incarnations of Genesis - the original line-up, fronted by Peter Gabriel, and the trio, led by drummer Phil Collins.
Anastasio called the band "rebellious, restless and constantly striving for something more".
He added: "Every musical rule and boundary was questioned and broken.
"It's impossible to overstate what impact this band and musical philosophy had on me as a young musician. I'm forever in their debt."
Gabriel did not attend the ceremony. Former bandmate Mike Rutherford said: "He has a very legitimate and genuine excuse. He's actually starting a tour."
One of The Hollies' founding members, Allan Clarke, recalled how, as a child, he told his father he was going to become a professional musician, only to be reminded that bands had a lifespan of three or four years.
"Well, Dad, I'm being inducted into a museum. How's that for longevity?" he joked.
Other inductees at the annual ceremony at The Waldorf-Astoria hotel were reggae superstar Jimmy Cliff and Iggy Pop and the Stooges.
Artists are only eligible for the Hall of Fame honour 25 years after the release of their first single.
Around 600 music industry professionals decide on who should be honoured.
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