I caught a New York Times headline about two soldiers who didn't get on with one another. This had disastrous consequences and whilst I have some experience of dealing with this sort of thing in business, I wondered how this would normally be dealt with in the military?
Normally, they would just battle it out and then shake hands and get on with the job! But there is the case of the SAS attack on Pebble island during the Falklands, two Sgts, who had a lon standing grudge against each other reached boiling point and a fight broke out amongst them!
It would depend upon the situation, the level of antagonism, effect on the others in the unit and whether they were in a combat zone. If their actions and behaviour was effecting the good running of the unit then the first call would be to the unit commander for a warning, If it continued then it would probably result in internal disciplinary action and punishment. If it carried on and involved physical violence, then a court martial. If not then the chances are that the officer in command would want shot of both of them, and they would be transferred out - to two seperate units. If in a combat zone, there is every possibility that the officer may threaten to shoot them on the spot if their actions affected the good running of the unit (though I don't think this actually happened). The commanding officer did have that power in a field courts martial.
