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Multiple-Phased Systems (MPS), i.e., systems whose operational life can be partitioned in a set of disjoint periods, called "phases", include several classes of systems such as Phased Mission Systems and Scheduled Maintenance Systems. Because of their deployment in critical applications, the dependability modeling and analysis of Multiple-Phased Systems is a task of primary relevance. The phased behavior makes the analysis of Multiple-Phased Systems extremely complex. This paper describes the modeling methodology and the solution procedure implemented in DEEM, a dependability modeling and evaluation tool specifically tailored for Multiple Phased Systems. It also describes its use for the solution of representative MPS problems. DEEM relies upon Deterministic and Stochastic Petri Nets as the modeling formalism, and on Markov Regenerative Processes for the model solution. When compared to existing general-purpose tools based on similar formalisms, DEEM offers advantages on both the modeling side (sub-models neatly model the phase-dependent behaviors of MPS), and on the evaluation side (a specialized algorithm allows a considerable reduction of the solution cost and time). Thus, DEEM is able to deal with all the scenarios of MPS which have been analytically treated in the literature, at a cost which is comparable with that of the cheapest ones, completely solving the issues posed by the phased-behavior of MPS.