Electrorheological (ER) fluids are fascinating materials that undergo dramatic reversible changes in their rheological properties upon the application of electric fields. In many proposed applications, the fluids will be subjected to a dynamic stimulus with finite deformation. We use a particle-level simulation method to investigate the dynamic behavior of monolayer ER fluids. ER fluids are linear viscoelastic for only very small strain amplitudes. The transition to nonlinear deformation arises from very slight rearrangements of unstable structures. At large strain amplitudes, the behavior is viscoplastic, while at large dimensionless frequencies (proportional to omega/E-0(2), where omega is the oscillation frequency and E-0 is the electric field strength), the response is Newtonian for all strain amplitudes. Simulation results agree qualitatively with experiments. The dependence of the flow behavior on the strain amplitude and dimensionless frequency is summarized in the form of a Pipkin diagram.