In this paper a new adaptive control approach is proposed for a class of systems represented by an unknown hysteresis nonlinearity preceding unknown linear dynamics. The existing adaptive inverse control framework relies on over-parametrization to handle the bilinearly coupled parameters of hysteresis and dynamics, which often results in prohibitively many parameters if faithful hysteresis models are adopted. The proposed scheme eliminates over-parameterization by adapting the hysteresis parameters and the dynamics-related controller parameters at different time scales, both much slower than the plant dynamics. The scheme shows promise in simulation of output tracking for a piezoelectric positioner, where the hysteresis nonlinearity is modeled by a Preisach operator. As a first step towards full analysis of the closed-loop system, an identification problem containing bilinear parameterization is analyzed. It is shown that multi-time-scale, slow adaptation leads to local, asymptotic parameter convergence under appropriate conditions.