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In December 2020, at the 2-m telescope of the Terskol branch of the Institute of Astronomy, we carried out spectrophotometric observations in the range of ~0.36–0.95 μm of nine asteroids of the Main Belt (19 Fortuna, 52 Europa, 102 Miriam, 177 Irma, 203 Pompeja, 250 Bettina, 266 Aline, 379 Huenna, and 383 Janina), which were near perihelia of their orbits with significant eccentricities, in order to determine the effect of maximum subsolar temperatures on them. The study of the reflecance spectra of asteroids showed that the mineralogy of their matter is low-temperature and basically corresponds to the previously established classification (Tholen, 1989; Bus and Binzel, 2002). But in the spectra of eight asteroids (with the exception of 102 Miriam), for the first time, significant deviations were found that go beyond the spectral boundaries of their taxonomic types in the absence of noticeable changes in the spectral transparency of the Earth's atmosphere at time intervals shorter and longer than the exposure time. Such features can be interpreted as light scattering by a mobile (or inhomogeneous) dusty exosphere that forms near these asteroids near perihelion in the process of ice sublimation at the highest subsolar temperatures. In addition, as follows from the data obtained from the GOES-16 and SOHO satellites, the considered asteroids at the end of November 2020 (10 days before the start of our observations) were affected by a strong solar flare in the X-ray range, and then by a shock wave in solar wind caused by a coronal mass ejection on the Sun, which was quasi-synchronous with the X-ray flare. This probably led to an additional increase in the sublimation activity of the asteroids and manifestations of a derivative dusty exosphere. [ABSTRACT FROM AUTHOR]