We're not sure why these two alligators decided to get into this nasty fist fight. One alligator is noticeably smaller than the other, so it could have something to do with the whole alligators-eat-their-young thing, but we'll let alligator digest figure that out.
In any case, it was a pretty intense scene. The big alligator goes after the smaller gator early in the four minute video, and as the cameraman inches closer, the smaller gator spends the rest of the time looking severely hurt -- although it does eventually manage to escape. A crowd starts to form, and one of the bystanders spends the whole time yelling "golly".
Here's a GIF of the start of the fight:
Consider this reason number 1,876 why you shouldn't mess around with alligators on the golf course (unless you're John Peterson).