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The title is a pun, "bananas" being slang for "crazy," as well as a reference to the phrase "banana republic", describing the film's setting, since a banana republic is a pejorative term for a country that is politically unstable, dependent on limited agriculture (e.g. bananas), and ruled by a small, self-elected, wealthy, and corrupt clique.
When Woody Allen was asked why the film was titled "Bananas", he jokingly answered "Because there are no bananas in it." Edit (Coming Soon)