Abstract: In this paper, an adaptive controller is designed for a class of strict-feedback nonlinear systems with periodically time-varying parametric uncertainties. The unknown periodic parameters are expanded into Fourier series and the coefficients are estimated by using a differential learning algorithm, and the backstepping design technique is applied to the controller design. S-class functions are introduced for eliminating the influence of truncation error and ensuring the tracking performance. In particular, the virtue control variables are differentiable due to the adoption of the S-class functions. Several different S-class functions are given and different control effects are produced by using them in the controller design. The theoretical analysis and numerical results show that the tracking of the system output is bounded to the desired one, while all the signals in the closed-loop system remain bounded.