A third of News Corporation investors voted against James and Lachlan Murdoch being re-elected to the board on Friday, newly released figures show.
Almost 35% voted against James Murdoch, who is the company's deputy chief operating officer, while 34% voted against his brother.
The vote is seen as a rebuke over News Corp's handling of the phone-hacking scandal at the News of the World.
News Corp chairman Rupert Murdoch received 14% of "no" votes.
The phone-hacking scandal in the UK led to the News of the World being shut down.
The newspaper had been illicitly hacking into the voicemail messages of prominent people including murder victims and celebrities as they looked for stories.
Critics of the Murdoch family, which has control of News Corp and its global newspaper and media assets, say that not enough was done to stop the phone hacking when the accusations arose.
Investors 'want change'
Many shareholders have called for changes at the top of the company.
Anne Simpson is a senior portfolio manager at the California Public Employees Retirement System (Calpers), which voted against James Murdoch.
"I think this really tells the board that investors are looking for change, they're looking for robust independence," she told the BBC World Service.
"They are quite properly expecting due process for all concerned, but the real concern is that this is a board in need of rejuvenation and it's really in need of some robust independent oversight."
The Murdoch family controls about 40% of votes, while another 7% are controlled by Saudi Prince Alwaleed Bin Talal.
Stripping out those votes, a majority of shareholders voted against the Murdoch brothers at Friday's meeting, the figures show.
However, despite the level of shareholder dissatisfaction, all 15 nominees to the board were re-elected.