A fight broke out on an American Airlines jet while passengers were trying to get off and make connections ... and it's all on video.

TMZ obtained footage of a violent brawl on an AA flight that landed in Miami ... and the video picks up with a man and a woman getting physical. TMZ.com

The man and woman put their hands on each other, the other male passenger rushes over to separate the two ... and then the guy shoves them into empty rows of seats and tells them to back off. TMZ.com

All the while, a flight attendant is heard trying to clear a path so folks in the back of the plane can deboard and make a connecting flight.

Folks sitting near where the fight broke out then started requesting someone call the police.

The ruckus seems to calm down and people continue deplaning as t

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