<p dir="ltr">The application of frequency-modulated radar signals for locating objects offers the advantage of using long-term probing radar pulses. Such signals ensure the required radiated power and simultaneously retain the required coverage range. The linear frequency modulation signal is presently among the most extensive applications. However, the matched filtering of this type of radio-pulse involves an unwanted effect of rather high levels (up to about minus 13 dB) of side lobes of the signal compressed at the processing block outlet. This effect may increase the probability of erroneous detection or masking lower-power signals with more powerful side lobes. There are several techniques of reducing the side lobe levels, the use of signals with nonlilear frequency modulation being one of them. As an example, we can mention the well known two-fragment signals consisting of time concurrent linear-frequency modulated fragments. However, the mathematical models presently used to describe such a signal are inadequate to describe fully the effects that may occur at the moment of changing over from one fragment of the signal to another. Such effects appear as jump-like changes in the frequency and the phase, which causes distortions in the signal spectrum, raises the level of the side lobes of the autocorrelation function and sharp drops of their levels. These effects have not been touched upon in well known researches (see Section I of this paper analyzing the literature concerned). The tasks and goals pursued in this investigation are formulated in Section II. Section III of the paper is concerned with the mechanism of efficient compensation of the effects revealed and its mathematical description based on mathematical modeling results. A new mathematical model of a nonlinear-frequency modulated signal has been developed, which takes into account the effects revealed. Unlike the known ones, the model proposed is capable of compensating the jumps of instantaneous frequencies and phases that are initiated by the moments when the frequency modulation velocities change on transition from one fragment of the signal to another.</p><p dir="ltr">It would be expedient to concentrate the further research effort on special methods of compensation of the revealed effects for signals containing more fragments and combinations of fragments of different modulation types (see the Conclusions of this paper).</p>