Which bully bit his tail off? Alligators can be extremely brutal to each other. It is not uncommon to see them missing chunks of tail and even entire limbs.They have one of he most robust immune systems in the animal kingdom and can survive gruesome injuries that other species would not. But that doesn't mean alligators don't feel pain. Yes, they have a complex nervous system and absolutely feel pain. Think of it this way, humans can also survive gruesome injuries but we sure feel pain. Some say