For a system with hysteresis, we present a parameterized hysteresis model and develop a hysteresis inverse. We then design adaptive controllers with an adaptive hysteresis inverse for plants with unknown hystereses, A new adaptive controller structure is introduced which is capable of achieving a linear parameterization and a linear error model in the presence of a hysteresis nonlinearity. A robust adaptive law is used to update the controller parameters and hysteresis inverse parameters, which ensures the global boundedness of the closed-loop signals for a wide class of hysteresis models. Simulations show that the use of the adaptive hysteresis inverse leeds to major improvements of system performance.