In a statement on social media, Bruce Willis' family said it was a "relief to finally have a clear diagnosis" and also expressed their "deepest gratitude for the incredible outpouring of love".
As per the family, the 67-year-old was diagnosed with aphasia - which causes difficulties with speech - last year, but this has progressed and he has been given a more specific diagnosis.
"Today there are no treatments for the disease, a reality that we hope can change in the years ahead," the statement said.
In a report, the actor Brian Cox, who starred in the film Red with Willis, was quoted as saying that the news was "very sad" and that the actor was "witty and a great performer".