  We study nonequilibrium charge transport in a double-barrier Josephson
junction, including nonstationary phenomena, using the time-dependent
quasiclassical Keldysh Green's function formalism. We supplement the kinetic
equations by appropriate time-dependent boundary conditions and solve the
time-dependent problem in a number of regimes. From the solutions,
current-voltage characteristics are derived. It is understood why the
quasiparticle current can show excess current as well as deficit current and
how the subgap conductance behaves as function of junction parameters. A
time-dependent nonequilibrium contribution to the distribution function is
found to cause a non-zero averaged supercurrent even in the presence of an
applied voltage. Energy relaxation due to inelastic scattering in the
interlayer has a prominent role in determining the transport properties of
double-barrier junctions. Actual inelastic scattering parameters are derived
from experiments. It is shown as an application of the microscopic model, how
the nature of the intrinsic shunt in double-barrier junctions can be explained
in terms of energy relaxation and the opening of Andreev channels.
