Alligators have large mouths and powerful tails. They tend to strike out with the powerful tail and latch on to their prey with the strength of their jaws. As a result, in dreams, alligators often represent the lasting effect that words (accusations, slander, criticism, etc.) can have when they latch onto an individual. This symbol can also speak of the significant impact that comes from being hit by the negative words of others, particularly when those words are based in lies and deception. Notice the word play or pun associated with this symbol - powerful tails represent powerful tales.
* Symbol meanings provided by www.mydreamstories.com should not be used as a dream dictionary. They are for reference only and both dreamer and interpreter should be careful to listen to the voice of Holy Spirit as to what any particular symbol means in any specific dream.