i am glad they were both neutered, that helps! No, they need not keep fighting. While the breed was originally a fighting dog, that was a very long time ago, and that instinct has largely been bred out, as they have ben mostly companion dogs for many decades now.

And if you recreate yourself as the "top" dog in the house, they won't have to fight over who is in charge, they can defer to you. With the right training, things can become peaceful again, it's all up to you!