The three studios have each declined to comment.
The suit, filed in federal court in Los Angeles on Friday, seeks a jury trial and alleges that the studios have violated provisions of the 2010 collective bargaining agreement that require that films produced in North America must also be scored in North America.
The lawsuit names “Interstellar,” which was produced by Warner Bros. and Paramount; Warner’s “Journey 2: The Mysterious Island”; and MGM’s reboots of “Robocop” and “Carrie” as being in violation of the master contract.
Hans Zimmer scored “Interstellar” and received an Oscar nomination in the category earlier this year.
The union is seeking damages for losses suffered by AFM members and a court order requiring the studios make appropriate contributions to health benefit funds.
AFM is represented by attorneys at the law firms Bredhoff & Kaiser, and Levy, Ford & Wallach.