It was formed by Mick Fleetwood and John McVie . After the other original members Peter Green and Jeremy Spencer left , they added to the group Christine McVie , Lindsay Buckingham , and Stevie Nicks , who helped to make the group very famous . In 1998 , Fleetwood Mac ( Mick Fleetwood , John McVie , Christine McVie , Stevie Nicks , Lindsey Buckingham , Peter Green , Jeremy Spencer and Danny Kirwan ) were inducted into the Rock and Roll Hall of Fame and performed at the Grammy Awards program that year .