This paper presents a general formalism for calculating the time-dependent current through a mesoscopic system coupled to two time-dependent leads. The formalism is based on the Keldysh nonequilibrium Green function technique and allows for arbitrary interactions in the mesoscopic region. The analysis shows that the time-averaged current is proportional to the integral of the time-averaged density of states weighted by the coupling to the leads, similar to the time-independent result of Meir and Wingreen. The results are illustrated using an exactly solvable non-interacting resonant-tunneling system, where the current exhibits non-adiabatic behavior in response to a voltage pulse. The paper also establishes a connection to recent linear-response calculations and studies of electron-phonon scattering effects in resonant tunneling. The analysis is applied to a non-interacting resonant-level model, where the current is shown to depend on the elastic transmission coefficient and the difference in occupation factors of the contacts. The paper also considers the wide-band limit, where the current is found to depend on the time-dependent bias and the energy-dependent properties of the system. The results demonstrate that the current can exhibit complex time dependence, including ringing effects and non-adiabatic behavior, in response to time-dependent perturbations. The paper concludes with a discussion of the implications of these results for the understanding of time-dependent transport in mesoscopic systems.This paper presents a general formalism for calculating the time-dependent current through a mesoscopic system coupled to two time-dependent leads. The formalism is based on the Keldysh nonequilibrium Green function technique and allows for arbitrary interactions in the mesoscopic region. The analysis shows that the time-averaged current is proportional to the integral of the time-averaged density of states weighted by the coupling to the leads, similar to the time-independent result of Meir and Wingreen. The results are illustrated using an exactly solvable non-interacting resonant-tunneling system, where the current exhibits non-adiabatic behavior in response to a voltage pulse. The paper also establishes a connection to recent linear-response calculations and studies of electron-phonon scattering effects in resonant tunneling. The analysis is applied to a non-interacting resonant-level model, where the current is shown to depend on the elastic transmission coefficient and the difference in occupation factors of the contacts. The paper also considers the wide-band limit, where the current is found to depend on the time-dependent bias and the energy-dependent properties of the system. The results demonstrate that the current can exhibit complex time dependence, including ringing effects and non-adiabatic behavior, in response to time-dependent perturbations. The paper concludes with a discussion of the implications of these results for the understanding of time-dependent transport in mesoscopic systems.