Special monsters occur randomly in monster battles. There's no way of knowing whether or not a special monster will be in the battle. Also, if a special monster does appear, the same chance you have of capturing a normal monster applies to the special monster. They are not harder to capture, just slightly more difficult to find. Special monsters are use to level up troop pets as well as heal the troop pet during troop wars. Special monsters are also a main ingredient when evolving your monsters. Rare monsters will require at least one special monster when evolving, whereas special - epic monsters will require up to 4 special monsters for evolution.