Animals in dreams may be associated with your instincts and inmost desires which are most of the times repressed and also with your physical characteristics. Therefore, the alligator may stand for strength, endurance, vigor. Emotionally, the alligator represents an individual who is not easy to impress, cold-blooded, powerful, tough, driven by reason and intellect.
The alligator in your dream may also mean deceit, treachery, slyness and stealth. If you were attacked by an alligator in your dream, this points to the fact that there are people around you in the real world who do not have the best intentions and want to harm you stealthily. If you are chased by an alligator in your dream, you feel threatened and fear not to be overcome by unseen danger.