Autodynes (AD) with frequency modulation (FM) belong to the class of autoparametric short-range radar systems (SBRL) with delayed feedback, in which, under the influence of their own radiation reflected from the location object, autodyne changes in the parameters of the generator occur: amplitude and frequency of oscillations. These changes cause specific distortions in the formation of signal and noise characteristics. This phenomenon, inherent in all types of generators with all the laws and methods of FM, creates problems in signal processing, narrows dynamic range of the autodyne system and limits the scope of AD, especially in the ranges of millimeter and shorter waves. As the radiation wavelength decreases, the period of the autodyne signal becomes comparable or even less than the delay time of the reflected radiation. For such conditions, there is currently no mathematical model of AM with FM, which provides an adequate description of the obtained results of experimentally observed phenomena and the search for ways to solve this problem. The purpose of the work is to summarize the results of research related to the development of a mathematical model of AM with FM based on the methods of the theory of systems with delay, and on its basis to study the signal and noise characteristics of an autodyne generator under the influence of its own reflected radiation with different FM laws, and also consider the influence of the nonlinearity of the modulation characteristics of real generators on the formation of autodyne signals. A general solution of the system of equations for a single-circuit FM oscillator is presented, taking into account intrinsic noise, as well as an arbitrary ratio of the delay time of the reflected radiation and the period of the autodyne signal. The results of studies of the dependence of the signal shape and the features of the formation of noise characteristics of IM on the parameters of the FM, its law and the distance to the location object, as well as the influence of the feedback parameter of the «generator - location object» system and the nonlinearity of the modulation characteristic on the formation of autodyne signals are presented. The results of experimental studies performed on the example of an 8-mm Gunn diode generator confirmed the conclusions of the theoretical analysis. The results of the performed studies allow, based on the given parameters of the used generators, to calculate the signal and noise characteristics of AM with FM, necessary for their correct use in advanced SLRS. In addition, the main requirements and recommendations for autodyne modules intended for FM SLBRL are formulated.