Dielectric elastomer tubes are employed as actuators by radial electric stimulus. Their functionality is affected by electromechanical instabilities, whose study was mainly limited to the analysis of the free energy Hessian. In this paper, we identify a different class of instabilities—prismatic diffuse modes—by employing the linearized theory of superposed deformations on finitely strained deformable dielectrics. We develop the equations that determine the onset of such modes, and show through numerical examples that the tube may enter diffuse states before the Hessian criterion fails. Moreover, we find that loading paths that are stable according to the Hessian method, can bifurcate into diffuse modes.