The two sides are battling over the right to use a robotic likeness of the two fictional barflies in a chain of airport Cheers-style bars.
George Wendt and John Ratzenberger, who played Norm and Cliff in the long-running US sitcom Cheers, are fighting Paramount Pictures over control of their characters.
The two sides are battling over the right to use a robotic likeness of the two fictional barflies in a chain of airport Cheers-style bars.
The US supreme court is expected to rule in the next fortnight whether it will hear the Cheers case or send it back to a court in Los Angeles.
Whatevere the outcome, legal observers say the case could have huge implications for the entertainment industry.
Lawyer Dale Kinsella told the Los Angeles Times: "If a studio acquires the right to license an actor's image cloaked in the outfit of character, then Warner Bros could use Harrison Ford's face to sell cigarettes or beer as long as he was dressed as Indiana Jones."
The two actors have been fighting the studio for almost a decade, claiming they created the characters and not the studio.
The case has bounced between the courts, with different judges ruling in favour of both parties.
The studio says actors who perform a role do not win legal rights to a character just because they are the character in the mind of the public.
New York lawyer Floyd Abrams, who took Paramount's appeal to the Supreme Court, told the newspaper: "Certainly it is not irrational for the people to think of the actors who played Norm or Cliff when they see one of these characters, but it's our view that federal copyright law protects Paramount's right to license the use of these characters."
In the past, singer Bette Midler and gravel-voiced Tom Waits, have used the law to prevent commercials exploiting their distinctive voices.
And a US game show hostess won more than $400,000 from Samsung Electronics over an ad which featured a robot with more than a passing resemblance to her.
Cheers, set in a fictional Boston bar, was America's leading sitcom for more than 10 years and made stars of actors Ted Danson, Woody Harrelson and Kelsey Grammar, who went on to star in his own sitcom Frasier.