This paper addresses adaptive control of sandwich non-linear systems having an unknown sandwiched dead-zone between the linear dynamic blocks, as illustrated by a hydraulic valve system. An adaptive hybrid control scheme for control of such sandwiched dead-zone systems is developed. The proposed control scheme employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with an adaptive dead-zone inverse to cancel the dead-zone effect for improving output tracking. Stability and tracking performance of the closed-loop control system are analysed. Simulation results are used to illustrate the effectiveness of the proposed adaptive dead-zone inverse controller.