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This paper presents a design method of adaptive fuzzy controllers using fuzzy neural networks (FNNs). The adaptive controller uses two FNNs. One FNN is used to identify a fuzzy model of the controlled object. The fuzzy control rules are designed with the linguistic rules of the fuzzy model and are incorporated into the other FNN. The response of the designed control system is checked with a linguistic response analysis proposed by the authors. An adaptive tuning of the control rules of the FNN controller is made possible utilizing the fuzzy model. Simulations using a controlled object with non-monotonic input-output characteristics are done to verify the proposed design method.