We have studied the current vs voltage curves (I-V characteristics) of a mesoscopic device consisting of two electrodes and a molecular wire. The wire Hamiltonian includes both electronic funneling and Coulomb repulsion within a Hubbard model that is treated at the Hartree-Fock level. The inclusion of electron repulsion is an extension of-our previous work that only considered the case of noninteracting electrons. We have found several important features in the calculated characteristics of the wire. These include (1) a staircaselike structure that strongly resembles that associated with Coulomb blockade in heterostructures and quantum dots, but that in the ease of the wire is associated with the discrete nature of the molecular resonances; (2) regions of negative differential resistance associated with increased localization of the molecular resonances. Our theoretical model includes a consistent treatment of the conduction in the linear and nonlinear regimes which remains valid even when the device is operated close to resonance. These results can be particularly relevant for a comparison with recent experiments on molecular wires.