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An equation is developed for the distortion of multi-tone FM signals caused by transmission through a network with nonlinear phase characteristics. A simplified form involving only one term is also given and the conditions of its applicability are discussed. The power spectrum of the distortion is derived for the case where the simpler form is valid. Thus, the distortion-to-signal ratio in any frequency band may be obtained. Applications are presented where the results are used to determine equipment linearity specifications and to determine the distortion which results from propagation through the ionosphere.