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Published 09:04 27 Aug 2014 BST
Updated 16:03 27 Aug 2014 BST
The couple pictured at this year's Grammy Awards in January
According to Rolling Stone, the couple last performed together at the Bridge School Benefit in October of 2013. The Bridge School, which educates children with sever physical impairments, was co-founded by the pair in 1986, inspired by their son Ben who suffers from Cerebral Palsy.
In Unknown Legend, Neil tells the story of how he met Pegi when she was working at a diner near his California ranch.
Neither party has yet commented on the split. Both Neil and Pegi were scheduled to play a North Carolina gig on September 13th, but Pegi's name has now been removed from the line-up.
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