Electric-field-induced instabilities in thin bilayers composed of either purely viscous or purely elastic films resting on a solid substrate are studied. In contrast to the electric-field-induced instability in a single elastict film, the length scale of the instability for elastic bilayers call be (ruled by changing, the ratios of the shear moduli, thicknesses, and dielectric permittivities of the films. Linear-stability analysis is employed to uncover the variations in the wavelength. The instabilities of the viscous bilayers follow different modes of interfacial evolution: either in-phase bending or antiphase squeezing. Linear and nonlinear analyses show that the mode type can be switched by changing the dielectric permittivities of the films. Nonlinear simulations find a number of intriguing interfacial morphologies: (a) an embedded upper layer in all array of lower layer columns, (b) upper layer columns encapsulated by lower layer beakers, (c) lower layer columns covered by the upper layer liquid resulting it] concentric core-shell columns, (d) droplets of upper liquid oil a largely undisturbed lower layer. and (1) evolution of two different wavelengths at the two interfaces of the bilayer. The simulated morphology types (a), (b) and (d) have been seen previously in experiments. (39,41,45) The effect of the film viscosities oil the evolution of the instability and final morphologies is also discussed.