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A superposition property of angle modulation is derived for a class of modulating waveforms. Angle modulation is a highly non-linear operation, with significant sideband energy arising from the interaction of the various modulation components. Thus, the type of linear superposition of sidebands which holds for amplitude modulation does not hold for angle modulation. It is shown that a different type of linear superposition does hold for an important class of angle modulating waveforms, namely those containing at least one periodic component. (Author).