  We consider a mesoscopic region coupled to two leads under the influence of
external time-dependent voltages. The time dependence is coupled to source and
drain contacts, the gates controlling the tunnel- barrier heights, or to the
gates which define the mesoscopic region. We derive, with the Keldysh
nonequilibrium Green function technique, a formal expression for the fully
nonlinear, time-dependent current through the system. The analysis admits
arbitrary interactions in the mesoscopic region, but the leads are treated as
noninteracting. For proportionate coupling to the leads, the time-averaged
current is simply the integral between the chemical potentials of the
time-averaged density of states, weighted by the coupling to the leads, in
close analogy to the time-independent result of Meir and Wingreen (PRL {\bf
68}, 2512 (1992)). Analytical and numerical results for the exactly solvable
non-interacting resonant-tunneling system are presented.
