This paper addresses the problem of tracking and diagnosing complex systems with mixtures of discrete and continuous variables. This problem is a difficult one, particularly when the system dynamics are nondeterministic, not all aspects of the system are directly observed, and the sensors are subject to noise. In this paper, we propose a new approach to this task, based on the framework of hybrid dynamic Bayesian networks (DBN). These models contain both continuous variables representing the state of the system and discrete variables representing discrete changes such as failures; they can model a variety of faults, including burst faults, measurement errors, and gradual drifts. We present a novel algorithm for tracking in hybrid DBNs, that deals with the challengesposed by this difficult problem. We demonstrate how the resulting algorithm can be used to detect faults in a complex system.