A class of nonlinear receiver structures is described for the detection of weak signals in non-Gaussian narrowband noise. In particular, the concept of a locally optimum receiver structure is extended to the ease of narrowband signal and noise models. A useful class of non-Gaussian narrowband noise models is developed for which the locally optimum receiver implementation is explicitly determined. These structures are shown to provide considerable improvement over conventional linear receiver structures. The basis of comparison is taken as the asymptotic relative efficiency (ARE). Unfortunately, the locally optimum receiver requires explicit{sl a priori}knowledge of the underlying noise distribution. To circumvent this difficulty a rather simple adaptive nonlinear receiver structure is described which attempts to adapt to the unknown prevailing noise environment. This adaptive receiver is shown to provide fairly efficient and robust performance in a wide variety of non-Gaussian narrowband noise environments.