This paper addresses the problem of global regulation of nonlinear lower-triangular systems with nonlinear parameterization. The uncertain parameters are assumed to be in an unknown compact set or unbounded. To solve this problem, we propose a novel time-varying control design for uncertain lower-triangular systems. The proposed controller guarantees that closed-loop system trajectories are well-defined and bounded. In addition, after a certain finite time, all of the closed-loop trajectories exponentially converge to the origin.