Tractable probabilistic models (TPMs) are appealing because they admit polynomial-time inference for a wide variety of queries. In this work, we extend the cutset network (CN) framework, a powerful sub-class of TPMs that often outperforms probabilistic graphical models in terms of prediction accuracy, to the temporal domain. This extension, dubbed dynamic cutset networks (DCNs), uses a CN to model the prior distribution and a conditional CN to model the transition distribution. We show that although exact inference is intractable when arbitrary conditional CNs are used, particle filtering is efficient. To ensure tractability of exact inference, we introduce a novel constrained conditional model called AND/OR conditional cutset networks and show that under certain conditions exact inference is linear in the size of the corresponding constrained DCN. Experiments on several sequential datasets demonstrate the efficacy of our framework.