We have studied the effect of the electrostatic potential on the current across a one-dimensional tight-binding molecular wire by solving self-consistently the Poisson and Schrodinger equations. The results indicate that electrostatic effects on the current are very important in the nonlinear regime. They manifest themselves through a strong variation of the voltage drop in the interfacial region compared to the linear ramp expected in the absence of charge in the wire and also in the nature of the current-voltage characteristics. (C) 2000 American Institute of Physics. [S0021- 9606(00)71215-3].