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We consider the system-level self-diagnosis of multiprocessor and multicomputer systems under the generalized comparison model (GCM). In this diagnosis model, a set of tasks is assigned to pairs of nodes and their outcomes are compared by neighboring nodes. The collections of all comparison outcomes, agreements and disagreements among the nodes, are used to identify the set of faulty nodes. We consider only permanent faults in t-diagnosable systems that guarantee that each node can be correctly identified as fault-free or faulty based on a valid collection of comparison results (the syndrome) and assuming that the number of faulty nodes does not exceed a given bound t. Given that comparisons are performed by the nodes themselves, faulty nodes can incorrectly claim that fault-free nodes are faulty or that faulty nodes are fault-free. In this paper, we introduce a novel neural networks-based diagnosis approach to solve this fault identification problem. The new diagnosis approach exploits the off-line learning phase of neural networks to speed up the diagnosis algorithm. We have implemented and evaluated the new diagnosis approach using randomly generated diagnosable systems. The new neural-network-based self-diagnosis approach correctly identified most of the faulty situations forming hence a viable addition or alternative to solve the GCM-based fault identification problem.