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In this paper, we consider moving target detection using a distributed multiple-input multiple-output (MIMO) radar on stationary platforms in nonhomogeneous clutter environments. Our study is motivated by the fact that the multistatic transmit-receive configuration in a distributed MIMO radar causes nonstationary clutter. Specifically, the clutter power for the same test cell may vary significantly from one transmit-receive pair to another, due to azimuth-selective backscattering of the clutter. To account for these issues, a new nonhomogeneous clutter model, where the clutter resides in a low-rank subspace with different subspace coefficients (and hence different clutter power) for different transmit-receive pair, is introduced and the relation to a general clutter model is discussed. Following the proposed clutter model, we develop a generalized-likelihood ratio test (GLRT) for moving target detection in distributed MIMO radar. The GLRT is shown to be a constant false alarm rate (CFAR) detector, and the test statistic is a central and noncentral Beta variable under the null and alternative hypotheses, respectively. Simulations are provided to demonstrate the performance of the proposed GLRT in comparison with several existing techniques.