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An analysis is presented on the output signal-to-noise ratios for the FM correlation systems having an FM detector in each input channel of a conventional correlator. The input consists of a frequency-modulated signal combined additively with stationary narrow-band Gaussian random noise. A general expression is derived for the output signal-to-noise ratio. A detailed calculation is made for the output signal-to-noise ratios when each input signal is a carrier frequency-modulated by a Gaussian random process and the integrating filter is of RC low pass. The dependence of the output signal-to-noise ratios on several parameters is discussed.