MySpace is being sued by the families of five teenage girls who it is claimed were sexually assaulted by men they met through the social networking website.
MySpace is a very popular website
The negligence and fraud suit against the popular site, owned by Rupert Murdoch's News Corporation, was filed at a court in Los Angeles.
It comes after a similar lawsuit was filed by the parents of a 14-year-old American girl last year.
Last year, MySpace increased security measures to protect its younger users.
In April 2006, the website hired a former prosecutor in the US Justice Department's internet child exploitation unit, Hemanshu Nigam, as its chief security officer.
It also made it impossible for users aged 18 and above to contact 14 and 15-year-old members, unless they knew the younger person's email address.
The girls involved in the latest lawsuits were all aged between 14 - the minimum age for a MySpace account - and 15.
"In our view, MySpace waited entirely too long to attempt to institute meaningful security measures that effectively increase the safety of their underage users," said Jason Itkin, a lawyer for one of the firms representing the families.
However Mr Nigam said that "ultimately, internet safety is a shared responsibility".
"We encourage everyone to apply common sense offline security lessons in their online experiences and engage in open family dialogue about smart web practices," he added.
News Corporation's shares rose 1.7% in Thursday trading.
It bought MySpace for $580m (£333m) in July 2005.