A general class of nonlinear systems containing multiple 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. Both delayed and undelayed versions of the input signal are allowed to enter into the system. 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 is delay-independent and 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.