The singer's management told the BBC Shelley died in Estonia, where he had been living.
His music inspired generations of musicians over a five-decade career with his band and as a solo artist, they said.
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Formed in Manchester, England in 1976, The Buzzcocks' 1977 self-released debut EP, Spiral Scratch, is regarded to be the first DIY punk record, and their ultra-hooky sound, and teen angst lyrics, have been influential ever since.
BBC News flagged a tweet by The Charlatans' singer Tim Burgess where he wrote about Shelley's songs, saying they were "perfect three-minute pop songs" that were "the soundtrack to being a teenager". (Shelley's) songs were important to me when I was a young man and they still are to me now. "You will be missed".
Tracey Thorn, formerly one half of dance music duo Everything But The Girl, also paid her respects, quoting from Buzzcocks track 16 Again.
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He tweeted: "Pete Shelley wrote flawless three minute pop songs".
She tweeted: "Oh God but I loved Buzzcocks".
The Buzzcocks, with Steve Diggle (L), Pete Shelley, Steve Garvey and Danny Farrant (rear) perform at "The Late Late Show with Craig Ferguson" at CBS Television City on July 24, 2006, in Los Angeles. "'But after all life's only death's recompense'".
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