We address two challenges in the task of tracking and diagnosing complex systems with mixtures of discrete and continuous variables: Accurate tracking and correct diagnosis of failures. 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). We show that the DBN structure can be generated from a temporal causal graph. These models contain both continuous variables representing the state of the system and discrete variables representing discrete changes such as failures; these models can represent 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 challenges posed by this difficult problem. We demonstrate how the resulting algorithm can be used to detect faults in a complex hybrid system.