The low-cycle fatigue model presented in the companion paper is employed for developing hysteresis and damage models for deteriorating systems. The hysteresis model performs strength reduction at a current displacement cycle by evaluating the loss in the energy dissipation capacity along the completed displacement path. Hence it is completely memory dependent. Pinching is accounted for implicitly by a reduced energy dissipation capacity in a displacement cycle. The model predicts the experimental results obtained from variable-amplitude tests reasonably well. Response analysis under earthquake excitations reveals that both the maximum displacements and the number of large-amplitude displacement response cycles increase significantly with the reduction in energy dissipation capacity, resulting in higher damage. Damage is defined as the deterioration in the effective stiffness of a displacement cycle, which is in turn related to the reduction in the energy dissipation capacity. A simple damage function is developed accordingly, consisting of displacement and fatigue components. It is observed that the fatigue component of damage is more significant than the displacement component for deteriorating systems under ground motions with significant effective durations. Copyright (C) 2003 John Wiley Sons, Ltd.