Anthony, who was acquitted of murder in the death of her young daughter Caylee, has been sued for defamation by Zenaida Gonzalez and Roy Kronk, who accuse her of "willful and malicious" damage to their reputations.
Gonzalez's suit alleges Anthony had claimed a similarly named nanny had kidnapped her daughter in 2008. It turned out the nanny didn't exist.
Kronk alleges Anthony's attorneys, in statements to the news media, falsely implicated him in her daughter's death.
Anthony's attorneys are seeking to have the complaints dismissed.
Anthony, who has been living out of sight since her 2011 acquittal, faces a deposition by attorneys for Gonzalez, the Orlando (Fla.) Sentinel reported. Gonzalez's lawyers say they've agreed not to publish the deposition or reveal when or where it will be taken, the newspaper said.
Anthony filed for bankruptcy this year, claiming nearly $800,000 in debts with just over $1,000 in assets.