The problem of adaptively detecting a range distributed target or targets in Gaussian interference is considered in this paper.It is assumed that a set of secondary data is available.Firstly,we derive the adaptive Rao and Wald tests with one-step detection algorithm,and find that both of them are of the same asymptotic performance as the GLRT one.Secondly,the Rao and Wald tests are derived by resorting to the two-step design strategy.To our surprise,our derivations show that all the Rao,Wald and GLR tests in the two-step design strategy are equivalent.Thirdly,the property assessments are presented.It is shown that these new detectors guarantee CFAR property with respect to the Gaussian noise.Finally,simulation results show that these results are accurate. The problem of adaptively detecting a range distributed target or targets in Gaussian interference is considered in this paper. It is assumed that a set of secondary data is available. Firstly, we derive the adaptive Rao and Wald tests with one-step detection algorithm, and find that both of them are of the same asymptotic performance as the GLRT one. Second, the Rao and Wald tests are derived by resorting to the two-step design strategy. To our surprise, our derivations show that all the Rao, Wald and GLR tests in the two-step design strategy are equivalent.Thirdly, the property assessments are presented. It is shown that these new trials guarantee CFAR property with respect to the Gaussian noise. Finally, simulation results show that these results are accurate.