[en] We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon interaction, we use perturbation theory to determine the time dependence of the dot population and the average current. The limit of strong coupling is accessed by means of a self-consistent time-dependent mean-field approximation. These complementary approaches allow us to investigate the dynamics of the inelastic effects occurring when the applied bias voltage exceeds the phonon frequency and the emergence of bistability.