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 feasible parameter domains are also specified to promote the practical use of the m‐BWBN model. Second, a seismic demand database is constructed by nonlinear time history analyses using the m‐BWBN model and many ground motions. Third, we propose a new DNN architecture and detailed training methodologies to learn the effects of the complex hysteretic characteristics on the peak seismic responses. Numerical examples of reinforced concrete structures are introduced to test the prediction performance and applicability of the proposed DNN model. The source codes, data, and trained models are available for download at http://ERD2.snu.ac.kr.