Google's parent company Alphabet is facing legal action over the way it allegedly handled sexual misconduct claims against two senior managers.
Separately two lawsuits have been filed by long-term shareholders which accuse Alphabet's board of being involved in attempts to cover up the claims.
Both legal claims want Alphabet to do a better job of uncovering and responding to misconduct.
Google declined to comment on the lawsuits or whether it will respond.
The legal action is believed to have been prompted by the way that Google handled misconduct claims made against former Android boss Andy Rubin and former search head Amit Singhal.
Both men are believed to have received large pay-offs after being investigated over the claims. Neither now works for Google.
Both Mr Rubin and Mr Singhal have denied the allegations.
The way Google handled the incidents prompted demonstrations by staff and led to thousands walking out of their offices in co-ordinated protests in November.
In response, Google boss Sundar Pichai apologised for the way it had acted in the past over allegations of inappropriate behaviour and promised improvements.
One lawsuit claims that Google operated a two-tier policy when handling reports of harassment or discrimination.
Ordinary workers were typically fired and gained no benefits, but similar behaviour by high-level executives would be tolerated until managers were exposed, at which point they were paid off and allowed to resign, allege legal papers.
The double standard meant Alphabet's board had not done its job properly and its actions had cost the company millions, said the lawsuit.
Mr Pichai's statement to staff last October said: "Over the past two years, we have terminated 48 people, including 13 senior managers and above for sexual harassment. None of these people received an exit package.
"And to clarify: in that time, we have also not provided any exit packages to executives who departed voluntarily in the course of a sexual harassment investigation."
Frank Bottini, an attorney representing one shareholder, said the lawsuit wanted to prompt action at the highest level in Alphabet.
"We'd like to see ... meaningful change in the tone at the company, the policies, the treatment of women, the reporting of sexual harassment and other issues," he told Reuters.