Disney boss Michael Eisner is facing opposition about his plan to step down in 2006.
Even stepping down is proving difficult for Mr Eisner
Roy Disney and Stanley Gold, who tried to unseat Mr Eisner earlier this year, have said they will push for him to be replaced by early 2005.
They complain that he has failed to deliver a successful strategy, and also have criticised his pay awards.
Observers, however, said it was likely that Mr Eisner would be able to remain see out his current contract.
Mr Eisner, who has led Disney for two decades, said last week that will not seek to renew his contract when it runs out in two years.
The decision to announce his departure meets with some of his detractors' desires.
Mr Eisner is said to have identified Disney president Robert Iger as the person he most would like to replace him.
But a number of influential public pension funds - who controlled a portion of the 43% of votes which were withheld from Mr Eisner in March - want the board to be more independent in picking someone for the top job.