I am facing this problem. I have two supervisors but they are arguing about the way I should carry my project. This morning it was really embaracing: "you are completely wrong! You do not understand a thing! I think she should do that this way!" And then they ask me witch one is right! I can't take a side! They are both my supervisors!
Each one calls me aside and start speaking bad about the other, searching for my support.
I am in the middle of a big battlefield! Don't know what to do....
I am still at the beginning and I do not know what advices should I follow. Actually, for me, they both make sense!

sorry to hear that. Such a horrible experience. But it sounds very familiar to me. First step is to tell them how this makes you feel and you do not want this to continue (in a better language of course ) and if that doesn't work, take one of them off of your list and get another supervisor, even if this means an external supervisor in your team. Good luck..

What a pain. 404 has some good advice. I hope this works. If not, I would be tempted to speak to your director of studies about this and see what he/she thinks. It is a miserable position for you to be in. Hope it gets sorted.

While I am not an actual PHD student, if I had managers behaving like this, I woudl be stating very clearly that this was putting me in an impossible position, and that they both had a responsibility to resolve this. Privately I would be deciding which supervisor was most useful to me, and requesting that the other be replaced with another supervisor.

I cannot imagine how difficult this has been for you.