Is it possible to combine mecanim animations?

I have two animations that I’m using in Mecanim - Run and Punch. But the punch animation is standing still and I want to be able to Run AND Punch without stopping. Is it possible to have the Run animate the legs while the punch animates the arms?

I had trouble with this as well and this is the answer I got. It is an awesome answer and I think you will benefit from this as well. Good luck!
(PS. Remember to check best answer :D)