  We extend the relation between random matrices and free probability theory
from the level of expectations to the level of fluctuations. We show how the
concept of "second order freeness", which was introduced in Part I, allows one
to understand global fluctuations of Haar distributed unitary random matrices.
In particular, independence between the unitary ensemble and another ensemble
goes in the large $N$ limit over into asymptotic second order freeness. Two
important consequences of our general theory are: (i) we obtain a natural
generalization of a theorem of Diaconis and Shahshahani to the case of several
independent unitary matrices; (ii) we can show that global fluctuations in
unitarily invariant multi-matrix models are not universal.
