A general class of uncertain nonlinear systems with time-varying and uncertain state and input delays is considered. The 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 non-affinely into the system dynamics as well as to have uncertainties coupled with it. The control design is based on dual controller/observer dynamic high-gain scaling with an additional dynamic scaling based on a singular-perturbation-like redesign to address the non-affine 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 only information about the time delays that is required in the control implementation is a bound on the rate of variation of time delays.