Robert 'Bob' Brunning (29 June 1943 – 18 October 2011) was a British blues musician. He is likely to be best-remembered for his short-lived role as original bass guitar player with the original version of Fleetwood Mac. After his short stint in Fleetwood Mac (playing on just one track on their first album), Brunning joined Savoy Brown. He later embarked on a career in teaching which lasted 30 years. He did not abandon music however, and played in the Brunning Sunflower Blues Band, Tramp, and later The DeLuxe Blues Band.

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