  We present an analysis of the transient electronic and transport properties
of a nanojunction in the presence of electron-electron and electron-phonon
interactions. We introduce a novel numerical approach which allows for an
efficient evaluation of the non-equilibrium Green functions in the time domain.
Within this approach we implement different self-consistent diagrammatic
approximations in order to analyze the system evolution after a sudden
connection to the leads and its convergence to the steady state. These
approximations are tested by comparison with available numerically exact
results, showing good agreement even for the case of large interaction
strength. In addition to its methodological advantages, this approach allows us
to study several issues of broad current interest like the build up in time of
Kondo correlations and the presence or absence of bistability associated with
electron-phonon interactions. We find that, in general, correlation effects
tend to remove the possible appearance of charge bistability.
