  An extended Keldysh formalism, well suited to properly take into account the
initial correlations, is used in order to deal with the time-dependent current
response of a resonant tunneling system. We use a \textit{partition-free}
approach by Cini in which the whole system is in equilibrium before an external
bias is switched on. No fictitious partitions are used. Besides the
steady-state responses one can also calculate physical dynamical responses. In
the noninteracting case we clarify under what circumstances a steady-state
current develops and compare our result with the one obtained in the
partitioned scheme. We prove a Theorem of asymptotic Equivalence between the
two schemes for arbitrary time-dependent disturbances. We also show that the
steady-state current is independent of the history of the external perturbation
(Memory Loss Theorem). In the so called wide-band limit an analytic result for
the time-dependent current is obtained. In the interacting case we propose an
exact non-equilibrium Green function approach based on Time Dependent Density
Functional Theory. The equations are no more difficult than an ordinary Mean
Field treatment. We show how the scattering-state scheme by Lang follows from
our formulation. An exact formula for the steady-state current of an arbitrary
interacting resonant tunneling system is obtained. As an example the
time-dependent current response is calculated in the Random Phase
Approximation.
