In the range of small strains, the behavior of piezoceramics is described by linear constitutive equations. Nonlinear behavior of a softening Duffing-oscillator can be observed when polarized piezoceramics are excited near resonance by weak electric fields. This research is focused on the description of the nonlinear effects at ranges of moderate strains, as they occur in such dynamic case. Using the experimental amplitude-frequency responses, the parameters of piezoceramics can be determined. It is difficult to decide on some of the nonlinear characteristics, for example the type of conservative or nonconservative nonlinearities. To overcome these problems, quasi-static experiments with moderate applied electric fields and stresses resulting in strains of the same order as those in the dynamic cases are performed. The observed hysteretic behavior can be described using common hysteresis models. A combination of the dynamic and hysteresis models suggests that the nonlinear dynamic effects are mainly based on hysteretic stress-strain behavior.