In this study, the authors analyse the performance of some constant false alarm rate (CFAR) detectors namely: the cell averaging-CFAR (CA-CFAR), greatest of CFAR (GO-CFAR), the smallest of CFAR (SO-CFAR), the smallest of OS and CA-CFAR (SOSCA-CFAR) and the OS and CA-CFAR greatest of (OSCAGO-CFAR) detectors in homogeneous and nonhomogeneous Weibull background with binary integration under the assumption of a known shape parameter. The nonhomogeneity is modelled by the presence of interfering targets and the presence of a clutter edge in the reference window. The authors derive close-form expressions of the probability of false alarm in the case of a homogeneous clutter environment. For a non-homogeneous environment, the performance of these detectors is investigated by means of Monte Carlo simulations. The obtained results showed that the best false alarm rate performance at clutter boundary is obtained for the OSCAGO and GO-CFAR detectors, whereas the SOSCA and SO-CFAR detectors present better performance for the interfering targets situation.