The band announced the passing away of the singer on their Facebook page.
"It is with deep sadness and regret that the family of Angels singer/songwriter Bernard 'Doc' Neeson - loving father, family member and friend to so many - announce he has passed away in his sleep at 7.15am, today, 4th June 2014."
Doc Neeson has been battling a brain tumour over the past 17 months.
His family posted messages remembering him as a "beautiful soul".
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"We love you Dad. You couldn't have made any of your sons more proud of you if you tried. May your beautiful soul rest in peace sweet angel, fly high," Neezon's children - Dzintra, Daniel, Aidan and Kieran - posted.
"Good Night, Sweet Prince, and flights of angels sing thee to thy rest," his wife, Annie wrote, quoting from William Shakespeare's 'Hamlet'.
