Williams, who was once a rising star in the Canadian Forces, was sentenced to life in prison in October 2010 after pleading guilty to the murders of Jessica Lloyd and Cpl. Marie-France Comeau.
Lloyd's brother, Andy, says he and Lloyd's mother, Roxanne, have filed a statement of claim in Belleville's Ontario Superior Court of Justice which, among other details, seeks damages for the mental suffering they say they've had to endure.
Andy Lloyd, 31, says the family wants a fast resolution to the suit so that they can put the experience behind them and move on with their lives.
He says the last two years have been "quite a struggle" and both he and his mother are seeing counsellors for the depression they've had to deal with.
In addition to the murders of Lloyd and Comeau, Williams was also convicted of two sexual assaults and dozens of fetish break-ins. The Canadian Forces stripped him of his rank after his conviction and burned his uniform.
Two other lawsuits have also been filed against him and his estranged wife by victims Laurie Massicotte and a woman whose name cannot be disclosed under a publication ban.
Both have alleged in their statements of claim that Williams secretly and fraudulently transferred assets to his wife in March 2010 after he was criminally charged.
The claims, which have not been proven in court, have been vigorously denied by Williams' wife in her statements of defence.