A general class of uncertain strict-feedback-like nonlinear systems with dynamic input nonlinearities is considered. The addressed nonlinear system structure can be viewed as a nominal system of strict-feedback-like form with its input signal given by an uncertain nonlinear function coupled with an uncertain nonlinear time-varying input unmodeled dynamics. The proposed controller is based on a scaling-based redesign of the dual dynamic high-gain scaling based output-feedback control design for strict-feedback-like systems. The scaling-based redesign introduces a dynamic state extension and an additional dynamic scaling based on a singular-perturbation-like structure to address the nonlinear uncertain dynamic input perturbation. The proposed approach provides a globally stabilizing output-feedback control design that is robust to the uncertain input unmodeled dynamics and functional and parameteric uncertainties allowed in the system structure.