We calculate the nonequilibrium conductance through a molecule or a quantum dot in which the occupation of the relevant electronic level is coupled with intensity $lambda$ to a phonon mode, and also to two conducting leads. The system is described by the Anderson-Holstein Hamiltonian. We solve the problem using the Keldysh formalism and the non-crossing approximation (NCA) for both, the electron-electron and the electron-phonon interactions. We obtain a moderate decrease of the Kondo temperature $T_K$ with $lambda$ for fixed renormalized energy of the localized level $tilde{E_d}$. The meaning and value of $tilde{E_d}$ are discussed. The spectral density of localized electrons shows in addition to the Kondo peak of width $2 T_K$, satellites of this peak shifted by multiples of the phonon frequency $ omega_0$. The nonequilibrium conductance as a function of bias voltage $V_b$ at small temperatures, also displays peaks at multiples of $omega_0$ in addition to the central dominant Kondo peak near $V_b=0$.
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