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This paper considers the class of detection problems having two inputs containing a common (signal) component. If a complete statistical description of these inputs is available, then well-known parametric techniques yield optimum detectors. If less is known about the inputs, various nonparametric schemes can be utilized. It is usually assumed that the inputs are stationary, but it is often possible to consider nonstationary inputs which can be regarded as stationary during any given test interval (quasi-stationary). Under these conditions, adaptive procedures may be devised to estimate some parameter associated with the input processes, permitting adjustment of detection threshold. In this paper adaptive parametric detectors of this type are analyzed and compared to a nonparametric detector [polarity coincidence correlator (PCC)] under the assumption of quasi-stationary inputs. In addition an adaptive PCC is shown to be nonparametric for a wider class of input processes then the original PCC and is at least as efficient as the original PCC under the restricted input assumptions. Although the parametric detectors are superior when used with the input processes for which they were designed, the nonparametric detectors are easier to implement and can be markedly superior under departures from input assumptions.