A general class of uncertain nonlinear systems with both state and input delays is considered. The considered system structure includes a core nominal system of triangular structure along with uncertain appended dynamics driven by the entire state of the system. The control input is allowed to enter nonaffinely into the system dynamics as well as to have uncertainties coupled with it. Both state and input delays are allowed to be time-varying and uncertain. The control design is based on our dual controller/observer dynamic high-gain scaling approach with an additional dynamic scaling based on a singular-perturbation-like redesign to address the nonaffine and uncertain nature of the input appearance into the system dynamics. The proposed approach yields a delay-independent robust adaptive output-feedback control design. The control implementation does not require knowledge of the time delays or any magnitude bounds thereof; the only information about the time delays that is required is a bound on the rate of variation of time delays.