Check out video posted by The Golf Club at Hilton Head Lakes in Hardeeville, SC ... where two gators were caught in a crazy tussle right on one of the fairways.

According to course officials, the action all went down last week on the 18th hole ... when one golfer captured the wild scene.

You can see in the vid ... the two gators bit into each other's faces -- and wouldn't let go, even after they violently twisted!!!

And, if the action caught on video wasn't crazy enough for you -- a witness says the battle went on for roughly 2 HOURS!!

Thankfully, nobody was hurt during the on-course action ... but it's unclear if golfers' scores survived the melee as well.