Abstract: The clutter is assumed to be of Weibull distribution or characterized by a log-normal distribution.It is presented that a detailed derivation of the formula about asymptotic relative efficiencies(ARE) of generalized sign test and MannWhitney detector are compared with optimum linear parametric detector.ARE is simulated by Monte Carlo simulation and Simpson numerical integral.The result shows that the two nonparametric detectors' ARE increase appreciably as the clutter distribution deviates from Rayleigh.The asymptotic performance is better in log-normal clutter than in Weibull clutter.In the same case, the asymptotic performance of MW is greater than that of GS detector.