A robust adaptive control scheme is proposed for a class of nonlinear systems represented by input-output models with unmodeled dynamics. The scheme does not require the unknown parameters to satisfy the linear dependence condition and parameter estimation is not needed. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of unmodeled dynamics and bounded disturbances. Moreover, the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.