To see an alligator in your dream represents dishonesty, deception, and a false facade. It may indicate that you should step back and reevaluate your position or view of a certain matter. It may also represent your ability to move between the material world of waking life and the emotional, repressed world of the unconscious. In addition, the alligator can symbolize the ability and talent to cure or revitalize.
To dream that you are running away from the alligator denotes your refusal to face a distressing or upsetting matter. You may be harboring a negative feeling. There is some potentially destructive emotion that you don't want to admit you possess.
According to biblical interpretations, an alligator means that you will fall victim to the sin of arrogance and vanity.