In this paper, we study a particular subclass of partially observable models, called quasi-deterministic partially observable Markov decision processes (QDET-POMDPs), characterized by deterministic transitions and stochastic observations. While this framework does not model the same general problems as POMDPs, they still capture a number of interesting and challenging problems and have, in some cases, interesting properties. By studying the observability available in this subclass, we suggest that QDET-POMDPs may fall many steps in the complexity hierarchy. An extension of this framework to the decentralized case also reveals a subclass of numerous problems that can be approximated in polynomial space. Finally, a sketch of -optimal algorithms for these classes of problems is given and empirically evaluated. Categories and Subject Descriptors I.2.11 [Artificial Intelligence]: Distributed AI--Multiagent systems; G.3 [Mathematics of Computing]: Probability and statistics--Markov processe...