  We describe the evolution of double degenerate binary systems, consisting of
components obeying the zero temperature mass radius relationship for white
dwarf stars, from the onset of mass transfer to one of several possible
outcomes including merger, tidal disruption of the donor, or survival as a
semi-detached AM CVn system. We use a combination of analytic solutions and
numerical integrations of the standard orbit-averaged first-order evolution
equations, including direct impact accretion and the evolution of the
components due to mass exchange. We include also the effects of mass-loss
during super-critical (super-Eddington) mass transfer and the tidal and
advective exchanges of angular momentum between the binary components. We cover
much the same ground as Marsh et al.(2004) with the additional effects of the
advective or consequential angular momentum from the donor and its tidal
coupling to the orbit which is expected to be stronger than that of the
accretor. With the caveat that our formalism does not include an explicit
treatment of common envelope phases, our results suggest that a larger fraction
of detached double white dwarfs than what has been hitherto assumed, survive
the onset of mass transfer, even if this mass transfer is initially unstable
and rises to super-Eddington levels. In addition, as a consequence of the tidal
coupling, systems that come into contact near the mass transfer instability
boundary undergo a phase of oscillation cycles in their orbital period (and
other system parameters). Much of the formalism developed here would also apply
to other mass-transferring binaries, and in particular to cataclysmic variables
and Algol systems.
