Unipolar electro-optic and nonlinear optical effects are observed in a nematic liquid crystal cell with broken inversion symmetry. The cell is bounded by two plates which produce electric surface polarizations normal to the plates. When the two surfaces are different a unipolar electrooptic effect is observed : the electric field-induced director distortions occur only for one polarity of the field and not for the opposite polarity ("optical diode" effect). Another manifestation of the symmetry breaking is strong second harmonic generation by the cell.