The simplest design, minimum dimensions, weight and cost of short-range radar systems (SRRSs) are provided by transceivers with an autodyne construction principle. In these SRRS, the functions of the transmitter and receiver are performed by a single cascade - an self-oscillator (just an autodyne - AD) connected directly to the antenna without any decoupling elements. The AD, which generates probing microwave oscillations and simultaneously receives a signal reflected from the target, is a single self-oscillating system «oscillator - target», in which the autodyne effect manifests itself, consisting in changes in the amplitude, frequency and phase of oscillations due to changes in the «external» parameters of the autodyne system: the distance to the target and the speed of its change. Therefore, AD belong to the class of auto-parametric systems with delayed feedback. An adequate description of all complex processes in such a system is possible only by methods of the theory of nonlinear oscillations. The analysis of the processes of formation of signal characteristics of blood pressure with various types of modulation is particularly difficult. Among them, amplitude (AM) and frequency (FM) modulation of radiation are most widely used in SRRS. At the same time, it should be noted that when one of the types of modulation of microwave oscillators is carried out, another type of modulation is inevitably present. One of them is usually undesirable (parasitic), since it causes distortion of the signal characteristics due to the main type of modulation. This review summarizes the results of studies of autodyne SRRS taking into account simultaneous AM and FM radiation. At the same time, a mathematical model of AD with AM and FM has been developed, which provides the possibility of calculating the characteristics of amplitude selection (CAS), the shape and spectrum of the autodyne signal for the general case of an arbitrary ratio of the delay time reflected from the radiation target and the period of the modulating function. The model is represented by a system of linearized in the vicinity of the stationary mode of an autonomous oscillator of differential equations with a lagging argument. These equations take into account the internal and external inertia of the autodyne system, due to the finite value of the rate of change of oscillation parameters of the oscillator and the finite time of propagation of probing radiation to the target and back, respectively. The transition from general expressions to specific expressions is performed for the case of simultaneous AM and FM autodyne according to the law of harmonic function. At the same time, the case of a strong inequality is considered а м , when the main spectral components at the frequency of а an autodyne signal are grouped not only in the region of low «zero» frequencies, but also in the vicinity of the harmonics of the modulation frequency м . Taking into account this inequality in the finite expressions describing the autodyne response, the decomposition of the delayed action functions into Taylor series is performed for a small delay time of the reflected radiation compared to the current observation time. This decomposition allowed us to move on to expressions in which all variables become explicit. As a result of the interaction of probing and reflected radiation from the target in the AD with harmonic AM on the harmonics of the modulation frequency, including the zero harmonic, output signals are formed depending on the distance to the target in the form of periodic CAS targets. If in AM AD the magnitude of the concomitant deviation of the generation frequency is negligible, then the maximum of the autodyne response corresponds to the middle of the CAS. At the same time, the efficiency of transferring the signal received from the target to the harmonics of the modulation frequency decreases with increasing harmonic number. If there is a concomitant deviation of the generation frequency in AM AD, when it increases, the region of the main maximum of the CAS first shifts towards large values of the normalized distance, and in the future - the appearance of a multi-humped CAS, characteristic of FM SRRS. The efficiency of signal transfer to the higher harmonics of the modulation frequency in AM AD improves somewhat with an increase in the concomitant frequency deviation. During the interaction of probing and reflected vibrations from the target in the self-oscillating system of an autodyne oscillator with harmonic FM on the harmonics of the modulation frequency, including the zero harmonic, the formation of periodic CAS of the targets occurs. If the values of the accompanying AM and the parameter of the external feedback of the autodyne system «oscillator - target» are negligible, then in FM AD, the formation of autodyne signals on the harmonics of the modulation frequency and in the vicinity of the zero harmonic occurs in accordance with the Bessel functions, similar to the formation of signals in homodyne FM SRRSs. The presence of concomitant (parasitic) AM radiation of FM AD makes changes in the amplitude and phase ratios of signals that cause deviations of the generated CAS of the target from the type of Bessel functions. At the same time, both in the presence of concomitant AM and in its absence at the edges of the CAS at the output of the FM AD, signals from the target are observed only at the zero harmonic modulation, i.e. in the Doppler frequency range. The influence of concomitant AM on the formation of CAS in autodyne FM SRRS decreases significantly with an increase in the harmonic number of the modulation frequency. Amplitude modulation in autodyne SRRS, both in the case of its deliberate use in AM SRRS, and in the case of FM SRRS, when AM is parasitic and undesirable, the amplitude values of signals in the middle part of the CAS at all harmonics of the modulation frequency, including the zero harmonic, increase asymptotically with the approach of the AM coefficient to unity. The spectrum of the signal of the autodyne SRRS with simultaneous AM and FM on the harmonics of the modulation frequency has an asymmetric appearance. If the value of the parameter of the external feedback of the autodyne system «oscillator - target» is commensurate with one, then the signals of AD with AM and/or FM from a point reflector moving uniformly and rectilinearly have anharmonic distortions. When creating promising autodyne transceiver modules for FM SRRS, it is necessary to take into account the noted features. First of all, measures should be taken to reduce the level of concomitant AM and the causes of signal distortion due to autodyne frequency changes. In addition, autodyne modules must provide the required linearity of the FM law in a wide band and repeatability of modulation characteristics in mass production conditions. Experimental data obtained on the example of hybrid-integral oscillator modules «Tigel-08» confirmed the results of theoretical studies and the adequacy of the developed models of autodyne SRRS with AM and FM. An additional confirmation of the validity of the developed model of autodyne SRRS with AM and FM is the successful operation of a number of radar systems, sensors and meters created on the basis of microwave K-band Gann-diode oscillators.