Dielectric elastomers (DEs) are a class of highly deformable electro-active polymers (EAPs) employed for electromechanical transduction technology. Imparting anisotropy to the material behaviour of DEs by adding soft fibres has become promising for suppressing the electromechanical instability besides enhancing the actuation performance. Practically dielectric elastomer based devices undergoes transient motion, making dynamic analysis a crucial aspect for the design of such actuators. In this work, we analyse the electro-viscoelastic response of a transversely isotropic dielectric elastomer subjected to suddenly applied constant and harmonic electric loads. A material model of anisotropic viscoelastic dielectric elastomers is presented by additively decomposing the isotropic free energy density corresponding to DE matrix and anisotropic free energy density corresponding to fibre into equilibrium and viscous parts. Based on the developed material model, equations governing the dynamic motion of the actuator is derived using the Euler-Lagrange equation for non-conservative system. Evolution equations consistent with the laws of thermodynamics are presented to obtain the isotropic and anisotropic viscous stretches. Developed dynamic model is utilized for describing the dynamic response, instability analysis, periodicity, and resonance properties of a dielectric elastomer actuator for different values of viscoelasticity and anisotropy parameters. Phase portrait and Poincarè maps are presented to analyse the periodicity of the nonlinear oscillations of the actuator. The results reveal that viscoelasticity delays the onset of dynamic pull-in instability. Simultaneously, a quasi-periodic to periodic transition is also achieved. The results presented can help in efficient and robust designing of dielectric elastomer based actuators subjected to dynamic loading. © 2020 IOP Publishing Ltd.