The effect of inelastic scattering, particularly that of the electron-phonon interactions, on the current-voltage characteristics of a one-dimensional tight-binding molecular wire has been investigated. The wire has been modeled using the Su-Schreiffer-Heeger Hamiltonian and we compute the current using the Landauer's scattering formalism. Our calculations show that the presence of strong electron-lattice coupling in the wire can induce regions of negative differential resistance (NDR) in the I-V curves. The reasons for this can be traced back to the quasidegeneracy in few of the low-energy molecular levels in the presence of electron-phonon coupling and an external applied bias. The molecular levels become highly delocalized at the critical bias at which the NDR is seen, corresponding to the vanishing of the electron-phonon coupling with equal bond lengths. (C) 2004 American Institute of Physics.