Analysis of constant false alarm rate (CFAR) detectors with noncoherent integration has been limited to the cell-averaging (CA) CFAR detector, the maximum mean level detector (MX-MLD) and the order statistics (OS) CFAR detector. Detection performance of the CA CFAR detector thal employs noncoherent integration has been studied by several authors even though the false alarm rate of the CA CFAR detector is sensitive to changes in the background clutter-plus-noise level under nonhomogeneous situations. Shor and Levanon analyzed the detection performance of the OS CFAR detector with noncoherent integration in homogeneous situation, but their formula requires numerical integration. In this paper, we extend the detection analysis to the generalized order statistics (GOS) CFAR detector that employs M-pulse noncoherent integration for general chi-square fluctuating targets in nonhomogeneous environments, which covers various OS and CA CFAR detectors. We obtain unified formulas of the false alarm and the detection probabilities for the GOS CFAR detector in closed form. By properly choosing the coefficients of the GOS CFAR detector, one can realize various kinds of CFAR processors, such as the CA CFAR detector, the OS CFAR detector, the censored mean level detector (CMLD) and the trimmed mean (TM) CFAR detector.