This paper studies the dynamic behavior of a dielectric elastomer balloon subject to a combination of pressure and voltage.  When the pressure and voltage are static, the balloon may reach a state of equilibrium.  We determine the stability of the state of equilibrium, and calculate the natural frequency of the small-amplitude oscillation around the state of equilibrium.  When the voltage is sinusoidal, the balloon resonates at multiple frequencies of excitation, giving rise to superharmonic, harmonic, and subharmonic responses.  When the frequency of excitation varies continuously, the oscillating amplitude of the balloon may jump, exhibiting hysteresis.