RDF Media asked a federal court Wednesday for more than $18 million in damages plus all "gains, profits and advantages" derived from the Fox show. The suit targets Fox Broadcasting and the show's producers.
The lawsuit claims the show, produced by Rocket Science Laboratories, "more aptly might be entitled 'Trading Copyrights' or perhaps 'Copyright Swap,'" and calls the Fox series "a blatant and wholesale copycat" of "Wife Swap."
Fox spokesman Scott Grogan said the network had not seen the lawsuit and could not comment.
"Wife Swap" first aired in Britain in 2003, where it was a hit. ABC bought the U.S. rights and announced its plans to air its own version, titled "Trading Moms."
In June, Fox announced plans to air its own version of the show with the title "Trading Spouses." Its show was widely criticized in the press as a copycat version of the planned ABC show.
ABC later changed the name of its program to avoid confusion with the Fox version, which aired first.
ABC is not a party in the lawsuit, but said in a statement: "We respect our producing partner's right to protect their intellectual property in whatever manner they deem most appropriate."
Earlier this year, producers of NBC's upcoming "The Contender" asked a judge to force Fox to edit allegedly unlawful bouts out of "The Next Great Champ" before it airs.
The producers claimed that "The Next Great Champ" was produced on a "rushed and frenzied basis" to beat NBC's series to the air and violated state boxing regulations.
Their attempt to keep the Fox show off the air was unsuccessful, although the series was a flop. NBC's "The Contender" begins airing in February.