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Sawyer died in Daytona, Florida, after "a brief illness", media are reporting.
The band is best known for songs including Cover of the Rolling Stone (on which Sawyer sang lead), Sylvia's Mother, and When You're in Love with a Beautiful Woman.
Sawyer joined Dr Hook in 1969, two years after he lost an eye in a car accident.
Despite not being the lead singer, his eye patch - and cowboy hat - meant he was the most easily recognised.
Sawyer left the band in 1981 to pursue a solo career,