Under French law, the damages related to legal proceedings could run into tens of thousands of euros and, in theory, the magazine editor and photographer could be sent to jail for a year.
Closer editor Laurence Pieau has already defended publication, insisting the photos were not in the least bit shocking, and has suggested that she has more intimate photos not yet published.
Italian magazine Chi - along with Closer, part of former Italian prime minister Silvio Berlusconi's Mondadori media group - printed a special edition featuring more than 20 pages of the photographs.
It carries a picture of the duchess, topless, on its front cover with a headline that reads: "The Queen is Nude!"
In an editorial the magazine's director, Alfonso Signorini, said he considered the photographs of the duchess to be "normal and up to date with the times".
They were "not particularly sensationalistic nor damaging to her dignity" and "surely makes her more likeable" and "less distant from all of us", he wrote.
Meanwhile, Irish Daily Star editor Michael O'Kane has been suspended while an internal investigation is carried out into the publication of the photographs.
The paper's co-owners - Britain's Northern and Shell group and the Dublin-based publisher Independent News and Media - have condemned the decision, saying they had no prior knowledge of it.
Richard Desmond, chairman of Northern and Shell, said he intended to withdraw from the Republic of Ireland and had begun steps to close down the joint venture.
A source at the Irish Daily Star said the belief there was that Northern and Shell would pull out of the publication on Tuesday, when a board meeting of the paper is scheduled to take place.
No British newspaper has printed the pictures, with the Daily Mail saying it had been offered similar pictures last week but had rejected them and the Sun saying that no responsible newspaper "would touch them with a bargepole".
The photographs were taken while the duchess was sunbathing on a private holiday with her husband at the French chateau of the Queen's nephew, Lord Linley, in Provence.
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