A general class of nonlinear systems containing delays in both state and input is considered and an output-feedback control design is proposed. The class of systems considered consists of a nominal system of feedforward form as well as appended uncertain dynamics. Both state and input delays are allowed to be time-varying and uncertain. The robust adaptive control design is designed based on our recent results on dual dynamic high-gain scaling based control designs for feedforward systems. 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.