A method is described for the efficient estimation of small overflow probabilities in nonMarkovian queueing network models. The method uses importance sampling with a state-dependent change of measure, which is determined adaptively using the cross-entropy method, thus avoiding the need for a detailed mathematical analysis. Experiments show that the use of rescheduling is needed in order to get a significant simulation speedup, and that the method can be used to estimate overflow probabilities in a two-node tandem queue network model for which simulation using a state-independent change of measure does not work well.