SEATTLE — Alphabet’s board of directors is investigating allegations of sexual misconduct and inappropriate relationships by current and former executives as part of its legal defense against shareholder lawsuits over its handling of the matters, according to documents viewed by The New York Times.

The internet giant’s board formed a Special Litigation Committee of independent directors this year and hired the law firm Cravath, Swaine & Moore to investigate the allegations made in one such shareholder lawsuit, according to the documents.

In a statement, Alphabet confirmed that its board had formed a committee “to consider claims made by shareholders in various lawsuits relating to past workplace conduct.” It did not elaborate further.

The board’s actions show how it is continuing to grapple with the fallout from the way it previously handled sexual harassment at Google, which is owned by Alphabet. The shareholder lawsuits followed a New York Times article last year that revealed Alphabet’s board had approved a $90 million exit package for a star executive, Andy Rubin, even though an investigation into a sexual harassment claim against him was deemed credible. The lawsuits accused the board of enabling the misconduct.