Dustin Lance Black won the original screenplay prize for "Milk," a biography of murdered gay-rights leader Harvey Milk.
The adapted screenplay award for "Slumdog Millionaire" went to Simon Beaufoy, who based it on a novel about an Indian street orphan's journey of survival and love.
"Slumdog Millionaire" has been an unlikely hit. The low-budget feature has 10 Oscar nominations, including best picture.
"Milk" has eight Academy Award nominations, including best picture and best actor for Sean Penn.
In television categories, writers for NBC's "30 Rock" and AMC's "Mad Men" won in the comedy and drama categories, respectively. Both also won WGA awards last year.
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