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The eight-person panel reached the decision Tuesday after hearing nearly a week of testimony about similarities between "Blurred Lines" - the biggest hit of 2013 - and Gaye's 1977 hit "Got to Give It Up."
Gaye's children sued Thicke and Williams, saying their song infringed the copyright of their father's song.
The singers denied copying Gaye's music.
"Blurred Lines" earned more than $5 million apiece for Thicke and Williams. Although both are credited as its songwriters, Williams wrote the song in about an hour in 2012, and the pair recorded it in one night.