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Alexander's major break in acting came in 1967 when she played Eleanor Backman in the original production of Howard Sackler's The Great White Hope at Arena Stage in Washington, DC. Like her co-star, James Earl Jones, she went on to play the part both on Broadway (1968), winning a Tony Award for her performance, and in the film version (1970), which earned her an Oscar nomination. Alexander's additional screen credits include All the President's Men (1976), Kramer vs. Kramer (1979), and Testament (1983), all of which earned her Oscar nods, Brubaker (1980), The Cider House Rules (1999), and Fur (2006).

Alexander portrayed Eleanor Roosevelt in two television productions, Eleanor and Franklin and Eleanor and Franklin: The White House Years, and she played FDR's mother, Sara Delano Roosevelt in HBO's Warm Springs with Kenneth Branagh and Cynthia Nixon, a role which garnered her an Emmy Award for Best Supporting Actress. Her other television movies include Arthur Miller's Playing for Time, co-starring Vanessa Redgrave, for which Alexander won another Emmy Award; Malice in Wonderland (as famed gossip-monger Hedda Hopper); Blood & Orchids; and In Love and War (1987) co-starring James Woods, which tells the story of James and Sybil Stockdale during Stockdale's eight years as a US Navy Commander and prisoner of war in Vietnam. Alexander currently plays the protagonist, Dr. May Foster, in the HBO drama series Tell Me You Love Me. Her character, a psychotherapist, serves as the connecting link between three couples coping with relational and sexual difficulties. The show's frank portrayal of "senior" sexuality and explicit sex scenes have generated controversy.

(wikipedia.org)