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This report considers the probability of detection off a target by a pulsed search radar, when the target has a fluctuating cross section. Formulas for detection probability are derived, and curves off detection probability vs, range are given, for four different target fluctuation models. The investigation shows that, for these fluctuation models, the probability of detection for a fluctuating target is less than that for a non-fluctuating target if the range is sufficiently short, and is greater if the range is sufficiently long. The amount by which the fluctuating and non-fluctuating cases differ depends on the rapidity of fluctuation and on the statistical distribution of the fluctuations. Figure 18, p. 307, shows a comparison between the non-fluctuating case and the four fluctuating cases considered.