In this paper, the adaptive dynamic surface control issue is addressed for a class of uncertain nonstrict-feedback nonlinear systems with asymmetric output constraints and input quantization. Firstly, nonlinear mapping, based on the hyperbolic tangent function, is introduced to handle output constraints. Then, radial basis function neural networks are employed to approximate the unknown nonlinear functions. Furthermore, with the help of Young’s inequality, only one learning parameter of neural networks needs to be tuned online at each step of recursion. Subsequently, the characteristic of a hysteretic quantizer is introduced to handle the input signals. Based on the quantizer and adaptive dynamic surface control technology, a specified neuroadaptive quantized control is developed for the nonstrict-feedback nonlinear systems, which guarantees all error signals are semi-globally uniformly ultimately bounded. Simulation results verify the effectiveness of the proposed means.