The Fox show, "virtually identical in format" to 'Wife Swap' according to RDF, follows two families as they swap wives and have to live in the other woman's home with her partner and children for two weeks.
The US show is made by production company Rocket Science Labs, which is also named in the Fox lawsuit.
'Trading Spouses' was first called into disrepute earlier this year when Fox confirmed plans to air the show two months before the US version of 'Wife Swap', called 'Trading Moms', was due to appear on the ABC Network.
Stephen Lambert, RDF's director of programmes, said: "In our view this is the most clear cut case of copyright theft in the history of the reality genre."
RDF's lawsuit alleges that Peter Chernin, president and chief executive of Fox parent News Corp, "told Fox executives in 2003 that he had seen the British version of 'Wife Swap' during a visit to London and that 'it was the show everyone was talking about in the UK'."
The suit alleges that executives from Fox and Rocket Science Labs decided to copy the 'Wife Swap' format "to confuse viewers and mislead them into watching 'Trading Spouses' rather than 'Wife Swap US'."
RDF says that 'Trading Spouses' "has a premise and format virtually identical to those of 'Wife Swap'", including the cast of characters, the structure of each airing of a complete swap, the sequence of events, the plot, the tone, the theme, the pace, the scene set-ups and the narration.
RDF also argues that the dialogue that arises from constructed situations, the contrasting settings, the structured before-and-after dialogue, the topics explored and the dramatic and comedic effect created by music are the same.
It even points the finger at the introductory segment and the opening graphics.
Fox has not yet issed a response to the lawsuit.
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