  We extend Teichmueller dynamics to a flow on the total space of a flat bundle
of deformation spaces of representations of the fundamental group of a fixed
surface S in a Lie group G. The resulting dynamical system is a continuous
version of the action of the mapping class group of S on the deformation space.
We observe how ergodic properties of this action relate to this flow. When G is
compact, this flow is strongly mixing over each component of the derormation
space and of each stratum of the Teichmueller unit sphere bundle over the
Riemann moduli space. We prove ergodicity for the analogous lift of the
Weil-Petersson geodesic local. flow.
