Kate and Gerry McCann are taking the action over comments made by the man who previously led the inquiry into Madeleine's disappearance.
In a statement, they said: "We - together with our three children Madeleine, Sean and Amelie - are taking this legal action against Goncalo Amaral over his entirely unfounded and grossly defamatory claims - made in all types of media, both within Portugal and beyond - that Madeleine is not only dead, but that we, her parents, were somehow involved in concealing her body."
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