Risk assessment in earthquake engineering necessitates effective predictive models for structural damage evolution, compatible with current decision support frameworks. Such models should be able to handle stochastic seismic excitations and responses, probabilistically associating earthquake features to structural damage. Fragility analysis is typically employed in this regard, serving as the basis for evaluating mean annual frequencies of measures that support decision-making. As recently shown by the authors, fragility functions are consistently captured by softmax function instead of the typically used lognormal distribution. This work expands these findings to dependent Markov models that generalize the classical structural fragility framework to account for longitudinal dependencies among multiple damage states, enabling damage prediction over the structural life-cycle. Featuring a specialized case of dynamic Bayesian networks, the suggested Markov models are dependent to some informative ground motion intensity measures and are modeled based on relevant longitudinal structural responses. Information over the structural damage states can be either complete or partial, which categorizes the corresponding approach into either a dependent Markov or a dependent hidden Markov model, respectively. The likelihood-based objectives can be computed by standard optimization, whereas in the presence of hidden states, solution can be found through Expectation-Maximization steps. Numerical results demonstrate the efficacy of the models to predict long-term damage evolution and it is seen that hidden models reveal more consistent transitions, by virtue of their structure that handles responses as uncertain damage indicators. The implementation details of each formulation are presented and practical suggestions are given.