Mathison's brother said she died of an illness.
Oscar-nominated screenplay writer, Melissa Mathison, died on Wednesday in Los Angeles.
Her brother, Dirk Mathison, said that his 65-year-old sister died after an illness, according to Variety.
Mathison earned an Oscar nomination for penning the screenplay for Steven Spielberg's 1982 film, E.T.: The Extra Terrestrial. She also served as an associate producer on the movie.
Most recently, she was working with Spielberg on an adaptation of Roald Dahl's 1982 children's tale, The BFG (Big Friendly Giant), which is in post-production and due out in 2016.
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"Melissa had a heart that shined with generosity and love and burned as bright as the heart she gave E.T.," Spielberg said in a statement obtained by Variety.
Mathison was married to Harrison Ford for 21 years, from 1983 to 2004, and has two children with the actor, Malcolm and Georgia.
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In addition to E.T, Mathison also wrote The Black Stallion (1979), The Escape Artist (1982), Martin Scorsese's Kundun (1997) and The Indian in the Cupboard (1995).
Mathison, who was born in Los Angeles and attended U.C. Berkeley, is survived by her two children, her brothers Dirk and Mark Mathison and her sisters, Melinda Johnson and Stephanie Mathison.