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We propose a novel methodology for fault detection and diagnosis in partially-observed Boolean dynamical systems (POBDS). These are stochastic, highly nonlinear, and derivative- less systems, rendering difficult the application of classical fault detection and diagnosis methods. The methodology comprises two main approaches. The first addresses the case when the normal mode of operation is known but not the fault modes. It applies an innovations filter (IF) to detect deviations from the nominal normal mode of operation. The second approach is applicable when the set of possible fault models is finite and known, in which case we employ a multiple model adaptive estimation (MMAE) approach based on a likelihood-ratio (LR) statistic. Unknown system parameters are estimated by an adaptive expectation- maximization (EM) algorithm. Particle filtering techniques are used to reduce the computational complexity in the case of systems with large state-spaces. The efficacy of the proposed methodology is demonstrated by numerical experiments with a large gene regulatory network (GRN) with stuck-at faults observed through a single noisy time series of RNA-seq gene expression measurements.