The comparative ease with which pure frequency modulation can be produced in electron oscillators at ultra-high frequencies has led to an examination of the problem of detecting a frequency modulated wave. In this region of frequencies the high ratio of frequency shift to modulating frequency gives rise to a very large number of side bands in the spectrum representing the modulated wave. Detection is usually accomplished by distorting the spectrum by means of a selective network and then impressing the output voltages upon the grid of a detector. This process is treated analytically and formulas are given which permit the calculation of low-frequency detection products in terms of the transmission characteristic of the distorting network and the maximum frequency shift during modulation. Measured detection products produced in such a system are compared with values calculated by means of the formulas which are given, and the results are shown to be in substantial agreement over the region in which certain simplifying assumptions are justified.