Alligators most always symbolize a problem! To kill or conquer one means you have overcome a problem. To be surrounded by one means you have to choose one bad thing to get out of a lot of bad things. (any way you run you will encounter at least one). To be eaten or killed by an alligator means the problem that is haunting you is likely to do you harm if not cured. To have a pet alligator symbolizes great control over one*s problems.