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In this paper, a method for the design of Hopfield networks, bidirectional and multidirectional associative memories with asymmetric connections, is proposed. The given patterns can be assigned as locally asymptotically stable equilibria of the network by training a single-layer feedforward network. It is shown that the robustness in respect to acceptable noise in the input of the constructed networks is enhanced as the memory dimension increases and weakened as the number of the stored patterns grows. More important is that the remembered patterns are not necessarily of binary forms. Neural associative memories for storing gray-level images are constructed based on the proposed method. Numerical simulations show that the proposed method is efficient for the design of Hopfield-type recurrent neural networks.