In this paper, for a class of uncertain nonlinear systems in the presence of inverse dynamics, output unmodeled dynamics and nonlinear uncertainties, a robust adaptive output-feedback controller design is proposed by combining small-gain theorem, changing supply function techniques with backstepping methods. It is shown that all the signals of the closed-loop system are uniformly bounded in biased case, and the output can be regulated to a small neighborhood of the origin in unbiased case. Furthermore, under some additional assumptions, an asymptotical result is obtained.