The capability of Dielectric Elastomers (DEs) undergoing large deformation is limited by electromechanical instability arising because of the positive feedback between the applied electric field and the reduction in thickness of the elastomer. This paper theoretically analyzes the stability of a dielectric elastomer fiber composite made up of two soft incompressible DE phases in the quasi-static and dynamic modes of actuation. An energy method, which relies on the energy balance at the position of maximum overshoot in an oscillation cycle, is used for extracting the critical electric field and stretch in the dynamic mode. The material behaviors of the fiber and matrix phases are characterized by neo-Hookean energy density function of the elastomer. The results demonstrate that DE composite with higher fiber volume fraction exhibits higher electric field at the onset of instability in both static and DC dynamic modes of actuation. The results of the present investigation can find potential applications in the development and design of the soft electroactive actuators subjected to dynamic loading. © 2021 Elsevier Ltd. All rights reserved.