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This paper presents a design method of adaptive fuzzy controllers using dual-fuzzy neural networks (DFNNs). For the convenience of adaptive control, the structure of the two-fuzzy neural-network controller is divided into two parts. Each part is a fuzzy neural-network (FNN). The adaptive controller uses two FNNs. One FNN is used to identify a fuzzy model of controlled object. The fuzzy control rule is designed with the linguistic rules of the fuzzy model and is incorporated into the other FNN. Simulations using a controlled object with an non-monotonic input-output characteristics are done to verify the proposed design method.