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There is a growing demand for fault diagnosis to increase the reliability of systems. Diagnosis by comparison is a realistic approach to the fault diagnosis of multiprocessor systems. In this paper, we consider n-dimensional hypercube-like networks for n ≥ 5. We propose an efficient fault diagnosis algorithm for n-dimensional hypercube-like networks under the MM comparison model by exploiting the Hamiltonian and extended-star properties. Applying our algorithm, the faulty processors in n-dimensional hypercubes, n-dimensional crossed cubes, n-dimensional twisted cubes, and n-dimensional Möbius cubes can all be diagnosed in linear time provided the number of faulty processors is not more than the dimension n.