This study deals with the tracking problem for a class of nonstrict-feedback switched nonlinear systems (SNSs) with unknown time-delay and unknown functions under arbitrary switching. To achieve this goal, an adaptive neural network-based dynamic surface control (DSC) based on backstepping approach is proposed. A neural network (NN) approximator based on radial basis functions (RBFs) is utilized to approximate unknown functions. Considering properties of Gaussian basis function in RBFNNs, an adaptive neural network DSC for nonstrict-feedback structure has been developed. A Lyapunov-krasovskii functional is applied to compensate the effect of unknown delay terms. Furthermore, a prescribed performance bound (PPB) control strategy is utilized to retain the tracking error within a predefined bound. Finally, a practical example is provided to prove the effectiveness of the proposed method. (C) 2020 Elsevier Ltd. All rights reserved.