An equation of motion for the amplitude of the perturbation of the interface of two incompressible fluids is obtained under the specification of small viscosities and small electrical conductivities. This equation describes the motion of a damped harmonic oscillator with the effects of the electric field given as: (1) a forcing function proportional to the displacement, and (2) a forcing function proportional to the time integral of the displacement. A stability analysis of this equation shows how the electrical conductivity, surface charge, frequency of the applied field, viscosity, surface tension, electric permittivity, fluid depth, and density affect the stability of the fluid interface. The destabilizing effect of the surface charge and the stabilizing effect of the viscosity are illustrated for dc and ac applied fields. It is shown that the minimum dc destabilizing voltage can be lower than the value given by Taylor and McEwan, and that instability can result with an ac field that is about 0.2 the strength of the destabilizing dc field.