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The nonlinear electrohydrodynamic stability of an irrotational jet in the presence of capillary force and weak viscous stress on the surface has been studied. Two nonlinear modiÿed Schr odinger equations are obtained. Neglecting the viscous stress, the classic Schr odinger equations are obtained. The stability conditions of steady state solutions are investigated, using the modulation concept. It is found that the viscous stress produces a resonance (say a viscous resonance) away from the critical point. For the progressive waves, we obtained modiÿed transition curves inserting the viscous stress. The classic nonlinear cuto wave number is obtained and this means that the viscous stress has a uctuating e ect on the perturbed jet, away from the critical points.