The paper discusses the time-dependent transport in mesoscopic systems coupled to two leads under the influence of external time-dependent voltages. The authors use the Keldysh nonequilibrium Green function technique to derive a formal expression for the fully nonlinear, time-dependent current through the system. The analysis allows for arbitrary interactions in the mesoscopic region but treats the leads as noninteracting. For proportionate coupling to the leads, the time-averaged current is derived as an integral between the chemical potentials of the time-averaged density of states, weighted by the coupling to the leads, similar to the time-independent result by Meir and Wingreen. Analytical and numerical results for an exactly solvable non-interacting resonant-tunneling system are presented. The current does not follow the driving signal adiabatically, resulting in a "ringing" current for voltage pulses and complex time dependence for harmonic driving voltages. The paper also establishes connections to recent linear-response calculations and earlier studies of electron-phonon scattering effects in resonant tunneling.The paper discusses the time-dependent transport in mesoscopic systems coupled to two leads under the influence of external time-dependent voltages. The authors use the Keldysh nonequilibrium Green function technique to derive a formal expression for the fully nonlinear, time-dependent current through the system. The analysis allows for arbitrary interactions in the mesoscopic region but treats the leads as noninteracting. For proportionate coupling to the leads, the time-averaged current is derived as an integral between the chemical potentials of the time-averaged density of states, weighted by the coupling to the leads, similar to the time-independent result by Meir and Wingreen. Analytical and numerical results for an exactly solvable non-interacting resonant-tunneling system are presented. The current does not follow the driving signal adiabatically, resulting in a "ringing" current for voltage pulses and complex time dependence for harmonic driving voltages. The paper also establishes connections to recent linear-response calculations and earlier studies of electron-phonon scattering effects in resonant tunneling.