The concepts of the PMC and BGM self-diagnosing system models of F. P. Preparata et al. (1967) and F. Barsi et al. (1976), respectively, including the notions of fault sets, consistency, and diagnosability number, are reviewed. Two one-step diagnosability algorithms are applied, one to the PMC model and the other to the BGM model. In both models, one-step diagnosability refers to a system's ability to determine all the faulty units from single collection of test results. Using the letters n, m, and tau to denote the number of units, the number of tests, and the diagnosability number, respectively, it is shown that in the BGM model the algorithm has a complexity of O(n tau /sup 2//log tau ), and, in the PMC model, the algorithm has a complexity of O(n tau /sup 2.5/). >