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This paper considers the problem of adaptive radar detection in Gaussian clutter with unknown spectral properties. We employ a Bayesian approach based on a suitable model for the probability density function (pdf) of the unknown clutter covariance matrix. We devise two detectors based on the generalized likelihood ratio test (GLRT) criterion both one-step and two-step. The suggested decision rules achieve the same performance as the non-Bayesian GLRT detectors when the size of the training set is sufficiently large. However, our new detectors significantly outperform their non-Bayesian counterparts when the training set is small. The analysis is also supported by results on real L-band clutter data from the MIT Lincoln Laboratory phase one radar and on high fidelity radar data from the knowledge-aided sensor signal processing and expert reasoning (KASSPER) program.