The stability of anisotropic electroactive polymers is investigated. A general criterion for the onset of instabilities under plane-strain conditions is introduced in terms of a sextic polynomial whose coefficients depend on the instantaneous electroelastic moduli. In a way of an example, the stable domains of layered neo-Hookean dielectrics are determined. It is found that depending on the direction of the electrostatic excitation field relative to the lamination direction, the critical stretch ratios at which instabilities may occur can be either larger or smaller than the ones for the purely mechanical case.