In this brief article, a novel combined backstepping and small-gain approach is presented to the global adaptive output feedback control of a class of uncertain nonlinear systems with unmodeled dynamics. The use of small-gain techniques permits removal of a common restriction, i.e. that the nonlinearities in the system are only dependent on the measured output. The design procedure is divided into two parts. In the first part, based on a partial-state observer, integrator backstepping is used to design an adaptive output-feedback controller which ensures robustness with respect to unknown parameters and uncertain nonlinearities. In the second part, it is shown that the adaptive controller can be made robust against dynamic uncertainties by means of recent nonlinear small-gain results.