A solution to the problem of output feedback stabilization has been developed a few years ago, for nonlinear systems which enjoy some strong observability property known as “uniform observability”, by using high gain observers. The present paper focuses on the same problem for systems which are NOT uniformly observable. More precisely an output feedback control design is proposed for such a system, which, on the one hand, is assumed to admit a stabilizing state feedback when the state is fully available, and on the other hand, admits an exponential observer when the control is appropriately chosen.