Jim Palmer in 1975 and 1976.
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Tom Glavine has won two Cy Young Awards, one in 1991, and the other in 1998.
Roger Clemens won seven Cy Young Awards during his career.
Koufax won three Cy Young Awards, 1963, 1965 and 1966. Starting in 1956 when the Cy Young Award was created, only one award was presented for the entire Major Leagues. After 1966, both the American and National Leagues presented Cy Young Awards.
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In 1973, Jim Palmer won his first of three Cy Young awards with a record of 22 - 9 and an ERA of 2.40.