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Manager Hillard Elkins said the 79-year-old actor, who was Bob in the critically acclaimed comedy Bob And Carol And Ted And Alice, was on a walk when he fell.
He was taken to a hospital and pronounced dead.
The actor's son was told he died of a heart attack, Elkins said, though police were unsure if the fall was medically related.
Los Angeles police Lt Robert Binder said no foul play was suspected. Binder said a jogger found Culp, who apparently fell and struck his head.
"The first born in every family is always dreaming of the older brother or sister he or she doesn't have, to protect, to be the buffer, provide the wisdom, shoulder the blows and make things right," he said. "Bob was the answer to my dreams. No matter how many mistakes I made on I Spy, he was always there to teach and protect me," Cosby said.
Candace Culp, the actor's ex-wife, said she was devastated. "He was a wonderful, creative man who contributed so much to his business, as an actor, as a writer, as a director," she said.
Robert Culp lately had been working on writing screenplays, Elkins said.