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In this paper, we introduce weak bisimulation in the framework of Labeled Concurrent Markov Chains, that is, probabilistic transition systems which exhibit both probabilistic and nondeterministic behavior. By resolving the nondeterminism present, these models can be decomposed into a possibly infinite number of computation trees. We show that in order to compute weak bisimulation it is sufficient to restrict attention to only a finite number of these computations. Finally, we present an algorithm for deciding weak bisimulation which has polynomial-time complexity in the number of states of the transition system.