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We consider model-checking algorithms for durational probabilistic systems, which are systems exhibiting nondeterministic, probabilistic and discrete-timed behaviour. We present two semantics for durational probabilistic systems, and show how formulae of the probabilistic and timed temporal logic Ptctl can be verified on such systems. We also address complexity issues, in particular identifying the cases in which model checking durational probabilistic systems is harder than verifying non-probabilistic durational systems.