This paper is concerned with the problem of adaptive tracking control for a class of switched stochastic nonlinear systems in nonstrict-feedback form with unknown nonsymmetric actuator dead-zone and arbitrary switchings. A variable separation approach is used to overcome the difficulty in dealing with the nonstrict-feedback structure. Furthermore, by combining radial basis function neural networks’ universal approximation ability and adaptive backstepping technique with common stochastic Lyapunov function method, an adaptive control algorithm is proposed for the considered system. It is shown that the target signal can be almost surely tracked by the system output, and the tracking error is semi-globally uniformly ultimately bounded in 4th" id="MathJax-Element-1-Frame" role="presentation" style="box-sizing: border-box; border-bottom: 0px; position: relative; min-width: 0px; text-align: left; border-left: 0px; padding-bottom: 0px; line-height: normal; text-transform: none; font-style: normal; text-indent: 0px; margin: 0px; min-height: 0px; padding-left: 0px; padding-right: 0px; display: inline-block; direction: ltr; max-width: none; word-wrap: normal; white-space: nowrap; float: none; letter-spacing: normal; max-height: none; font-size: 14.4px; border-top: 0px; font-weight: normal; border-right: 0px; word-spacing: normal; padding-top: 0px" tabindex="0">$4^{th}$ moment. Finally, the simulation studies for a ship maneuvering system are presented to show the effectiveness of the proposed approach.