We study ergodic theorems for disjoint C*- and W*-dynamical
systems, where disjointness here is a noncommutative version of the concept
introduced by Furstenberg for classical dynamical systems. We also consider
speci c examples of disjoint W*-dynamical systems. Lastly we use unique
ergodicity and unique ergodicity relative to the xed point algebra to give
examples of disjoint C*-dynamical systems.