Structural reliability assessment for a building accumulating damage in multiple seismic events can play a role in decision-making, for example, during a seismic sequence and/or for prioritizing post-earthquake repair operations. One of the models required for such an assessment is the probability that the structure will transit from one damage state to another, because of a shock of given intensity. Such a model is represented by a set of so-called state-dependent fragility functions, which are often evaluated via dynamic analysis of a nonlinear structural model. Developing the fragility curves in this fashion requires that one or more response measures allow to identify damage accumulation. One typically used seismic demand parameter is the peak transient inelastic displacement, for example at roof level. Although the practice of associating damage states to inelastic displacement thresholds is well-established for deriving classical fragility models, which consider the intact building as the initial state and failure the result of only a single transition, past research has indicated that more than one response parameter may be needed to assess state-dependent fragility. The present paper uses a series of inelastic single-degree-of-freedom systems, each having different natural period of vibration and post-hysteretic behavior, to investigate the use of supplementary seismic response measures for the definition of transitions between damage states in numerical dynamic analyses. More specifically, the residual displacement and measures of stiffness and strength deteriorating caused by ground shaking, are considered. The study employs back-to-back incremental dynamic analysis to simulate two consecutive damaging shocks. The analyses are used to calculate the strength and/or stiffness deterioration that can be associated with traditional ductility demand thresholds per damage state. Results show that damage accumulation over two shocks, expressed in terms of overall strength and stiffness loss, is hardly effectively represented by the peak inelastic excursion alone. This observation leads to the conclusion that to adjudicate a damage state transition from numerical analysis results, some response quantity that reflects the change in the dynamic properties of the structure due to the first damaging shock, should be also considered.