The trio was found guilty of copyright infringement after soul legend Marvin Gaye's kids claimed their summer hit was a rip off of their father's 1977 tune Got to Give It Up.
That verdict went down in March, 2015 at the end of a jury trial, and the Gaye heirs were awarded $5.3 million (GBP4 million) in actual damages and profits.
The Blurred Lines songwriters promised to appeal and on Wednesday (24Aug16), Williams, Thicke and rapper T.I. filed their opening brief at the 9th Circuit Court of Appeals. They are hoping to persuade lawmakers to overturn last year's judgment.
In their legal response, the appellants claim the outcome of the trial could "chill musical creativity and inhibit the process by which later artists draw inspiration from earlier artists to create new popular music".
If the Court of Appeals refuses to reverse the trial verdict, Thicke and his fellow songwriters are asking lawmakers to reduce the millions of dollars awarded in this case, contending actual damages and profits are not supported by "competent evidence".
The Gaye family is expected to vigorously fight the appeal.