Zsa Zsa Gabor and Frederic Prinz von Anhalt's son died a week after getting in an accident the same day Zsa Zsa died ... TMZ has learned.

Frederic tells us he and Zsa Zsa's adopted son, Oliver Prinz von Anhalt, died Sunday in a hospital following a motorcycle accident on Mulholland Drive.

That accident occurred the same day Zsa Zsa had a fatal heart attack. Oliver's motorcycle collided with a car.

We're told Oliver was in a coma and never came out.