The adaptive control problem of high-order time-delay nonlinear systems with lower-triangular or upper triangular structure is studied in this paper. Remarkably, by using the function scaling gain strategy and homogeneous domination method, two kinds of explicit universal adaptive controllers are designed such that all the states of the closed-loop system are globally bounded and the solutions of the original system converge to zero. The robust adaptive controller is also designed by employing the a-modification method. Examples are provided to demonstrate the validness of the theory. (C) 2017 Elsevier Ltd. All rights reserved.