- Had relationship with Princess Stéphanie of Monaco in 80s.
- Had a relationship with Valérie Kaprisky in the 1980s.
- Two daughters, Lou (born 4 February 1996) and Liv (born 25 August 2001) with Sophie Clerico.
- Has dual citizenship: French and American.
- Grew up in France.
- Anthony and Sophie Clerico separated in 2012 after 17 years.
- Anthony's autobiography Le Premier Maillon was published in 2008.
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