Many systems must operate in the presence of delays both internal to the system and in its inputs and outputs. In this paper we present a robustness result for mildly nonlinear systems. We use this result to show that for small unknown input delays, a simple adaptive controller can produce output regulation to a neighborhood with radius dependent upon the size of the delay. This regulation occurs in the presence of persistent disturbances and the convergence is exponential. We conclude with an example to illustrate the behavior of this adaptive control law.