A mathematical model of the autodyne radar with frequency modulation has been developed. The model is presented in the form of a self-excited oscillator with single-loop oscillating system adjusted in terms of frequency by varying the varicap capacitance. This model takes into account the impact of intrinsic radiation reflected from the object of location and inherent noises of the generator, as well as the power source noises. Basic expressions were derived for the calculation of the signal accompanying the spurious response of generator, components of the legitimate signal and the noise during the registration of autodyne response both in the power supply circuit and in terms of the variation of oscillation amplitude. Calculations of noise characteristics were carried out at small and large values of the feedback parameter. The phenomenon of periodic nonstationarity of noise levels at the autodyne generator output was detected in conditions of strong feedback. The results of calculations and experiments were obtained for the autodyne built on an 8 mm-band Gunn diode