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Soft dielectric elastomer actuators (DEAs) exhibit interesting muscle-like behavior for the development of soft robots. However, it is challenging to model these soft actuators due to their material nonlinearity, nonlinear electromechanical coupling, and time-dependent viscoelastic behavior. Most recent studies on DEAs focus on issues of mechanics, physics, and material science, while much less importance is given to quantitative characterization of DEAs. In this paper, we present a detailed experimental investigation probing the voltage-induced electromechanical response of a soft DEA that is subjected to cyclic loading and propose a general constitutive modeling approach to characterize the time-dependent response, based on the principles of nonequilibrium thermodynamics. In this paper, some of the key observations are found as follows: 1) Creep exhibits the drift phenomenon, and is dominant during the first three cycles. The creep decreases over time and becomes less dominant after the first few cycles; 2) a significant amount of hysteresis is observed during all cycles and it becomes repeatable after the first few cycles; 3) the peak of the displacement is shifted from the peak of the voltage signal and occurs after it. To account for these viscoelastic phenomena, a constitutive model is developed by employing several dissipative nonequilibrium mechanisms. The quantitative comparisons of the experimental and simulation results demonstrate the effectiveness of the developed model. This modeling approach can be useful for control of a viscoelastic DEA and paves the way to emerging applications of soft robots.