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The response of a hysteretic system is determined not only by the instantaneous external force but also by the loading history; thereby, a nonlinear time history analysis is needed for the accurate prediction of dynamic responses. The authors recently developed deep neural network (DNN) models for near‐real‐time seismic response predictions of hysteretic systems (Kim et al., 2019). The DNN models outperform existing regression‐based prediction methods for the idealized hysteretic systems used for the training. Structural systems often show complex hysteretic behavior such as degradation (in stiffness or strength) and pinching effects. In this paper, we develop DNN models for hysteretic systems having degradation and pinching. First, a new Bouc‐Wen class model, termed a modified Bouc‐Wen‐Baber‐Noori (m‐BWBN) model, is proposed to introduce the yield strength as an explicit model parameter. The …