  In the preceding paper of this series of articles we established peakedness
properties of a family of coherent states that were introduced by Hall for any
compact gauge group and were later generalized to gauge field theory by
Ashtekar, Lewandowski, Marolf, Mour\~ao and Thiemann.
  In this paper we establish the ``Ehrenfest Property'' of these states which
are labelled by a point (A,E), a connection and an electric field, in the
classical phase space. By this we mean that i) The expectation value of {\it
all} elementary quantum operators $\hat{O}$ with respect to the coherent state
with label (A,E) is given to zeroth order in $\hbar$ by the value of the
corresponding classical function O evaluated at the phase space point (A,E) and
ii) The expectation value of the commutator between two elementary quantum
operators $[\hat{O}_1,\hat{O}_2]/(i\hbar)$ divided by $i\hbar$ with respect to
the coherent state with label (A,E) is given to zeroth order in $\hbar$ by the
value of the Poisson bracket between the corresponding classical functions
$\{O_1,O_2\}$ evaluated at the phase space point (A,E).
  These results can be extended to all polynomials of elementary operators and
to a certain non-polynomial function of the elementary operators associated
with the volume operator of quantum general relativity. It follows that the
infinitesimal quantum dynamics of quantum general relativity is to zeroth order
in $\hbar$ indeed given by classical general relativity.
