Say no to blows and insults

To be understood, you need to speak clearly to them

Lay down certain rules: they have the right to argue, and you understand that everyone has to express their resentment, hurt and bitter feelings. But they don't hit each other, insult each other or humiliate each other. And tell them what the punishments are for each, depending on how serious their behaviour (anything from sending each one to their rooms for a set period of time to banning them from watching TV, going on the computer or anything that's important to them).  

Stick to the rules you set down (it's easier said than done!). If you waver, not only will they think you don't put what you say into practice but you'll also lose your authority. Hesitation and wavering in parents means a loss of reference points in children, and it also aggravates the situation you're trying to defuse.

And don't forget: unless you've been at the fight scene right from the start and you can clearly see who was the protagonist or who is in the wrong, don't punish one without punishing the other: they're both involved in the tiff and if both of them (or all of them, if there are more than two involved) were arguing, they should all be punished.