We investigate models of molecular junctions which constitute minimal
Hamiltonians to account for zero-bias-anomaly and the satellite features of
inelastic transport by molecular phonons. Through nonlinear transport
calculations with the imaginary-time nonequilibrium formalism, a HOMO-LUMO
model with Anderson-Holstein interaction is shown to produce co-tunneling
conductance peak in the vicinity of Kondo resonance which is mediated by a
re-emergent many-body resonance assisted by phonon excitations at bias equal to
the phonon frequency. Destruction of the resonance leads to
negative-differential-resistance in the sequential tunneling regime