This paper deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation. By exploiting solution properties of the differential equation and combining those properties with adaptive control techniques, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision. Simulations performed on a nonlinear system illustrate and clarify the approach.