If you are talking about dogs, there can only be one pack leader. He will never stop harassing and fighting another that is considered a threat to being the pack leader. Females will fight over territorial ares that pet owner will sit or sleep. If my lady is asleep and I come into bedroom with my dog, her dog growls, snarls, and attempts to fight my dog. But both alpha females get along when its only me taking care of them or vice-versa. When my lady and I sit on couch, one has to be on her side Andy dog has to be next to me. Otherwise, the territorial issue arises. Recently had to take her dog to vet for thirteen stitches to neck. My dog clamped on to her neck and would not let go. Finally I pulled my dogs ears and tail to make her let go. Pretty scary.