  The theory of real-time quantum many-body dynamics as put forward in Ref.
[arXiv:0710.4627] is evaluated in detail. The formulation is based on a
generating functional of correlation functions where the Keldysh contour is
closed at a given time. Extending the Keldysh contour from this time to a later
time leads to a dynamic flow of the generating functional. This flow describes
the dynamics of the system and has an explicit causal structure. In the present
work it is evaluated within a vertex expansion of the effective action leading
to time evolution equations for Green functions. These equations are applicable
for strongly interacting systems as well as for studying the late-time
behaviour of nonequilibrium time evolution. For the specific case of a bosonic
N-component phi^4 theory with contact interactions an s-channel truncation is
identified to yield equations identical to those derived from the 2PI effective
action in next-to-leading order of a 1/N expansion. The presented approach
allows to directly obtain non-perturbative dynamic equations beyond the widely
used 2PI approximations.
