This study proposes an adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">subsystem-based control</i> (SBC) for systematic and straightforward nonlinear control of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> th-order strict-feedback form (SFF) systems. By decomposing the SFF system to subsystems, a generic term (namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stability connector</i> ) can be created to address dynamic interactions between the subsystems. This 1) enables modular control design with global asymptotic stability, 2) such that the control design and its stability analysis can be performed locally at a subsystem level, 3) while avoiding an excessive growth of the control design complexity when the system order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> increases. The above properties make the proposed method suitable especially for high-order systems. We also design a smooth projection function for the system parametric uncertainties. The efficiency of the method is demonstrated in simulations with a nonlinear 5th-order system.