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An analysis of the effect of hard limiting on a sum of three or four sinusoidal signals has been performed. Analytic expressions are obtained for the output amplitudes for three input signals, two of equal amplitude, and for four signals, amplitudes equal in pairs. The results are compared with previous investigations that employ digital computer simulation, and excellent agreement is obtained. The signal suppression is investigated, and the "negative suppression" effect found numerically by other authors is shown to arise from logarithmic terms in the dependence of the output amplitude on the input signal amplitude ratio. These results should aid in understanding the interactions that occur when a limiting communications receiver is addressed by several signals.