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The work reported in the paper is part of Rand's broad studies of radar signal-processing methods. Models of radar clutter interference are developed which are both physically reasonable and more general than the usual Gaussian model or linear-process model. These are called conditionally linear processes. The major contribution of this paper is the development of simple conditions under which linear functionals of data generated by the model will have a Gaussian distribution. The result enables the computation of detection probabilities and false alarms for linear signal detectors.