This paper quantifies the impact of the non-stationary content (time-varying parameters that are not captured by power spectral content alone) of different ground-motion types (near/far field, with/without pulses time-series) on the nonlinear dynamic response of reinforced concrete bridge piers, taking into account the material cyclic degradation. Three groups of ground motions are selected to represent far-field, near-field without pulse and near-field pulse-like ground motions. Three analysis cases are considered corresponding to acceleration series matched to the mean response spectrum of: (1) far field, (2) near-field without pulse and (3) near-field pulse-like ground-motions, respectively. Using the selected ground motions, several nonlinear incremental dynamic analyses of prototype reinforced concrete bridge piers with a range of fundamental periods are conducted. Finally, a comparison between the response of the structures using the material model accounting for both buckling and low-cycle fatigue of reinforcing steel and the more conventional material model that does not account for these effects is made. The results show that the inelastic buckling and low-cycle fatigue have a significant influence on the nonlinear response of the RC bridge piers considered and that pulse effects can increase the mean acceleration response by about 50%.