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Modern models of cometary nuclei and their atmospheres as well as parameters of orbital motion of comets indicate the presense of extremal states in such objects of the Solar System. It is shown that: 1).The temperature distribution of the cometary gas has the minimum, in the range of 5-10 K, in the inner coma. This may cause the observed anomaly distribution of emission of Na I atoms in the heads of such bright comets like comet Mrkos 1957d/1957 V. 2). High-velocity collisions, V>70 km/s, betweeen cometary and interplanetary dust particles can lead to generation of short-living high-temperature (>100 000 K) plasma clots in the dust coma of comets, that will be accompanied by generation of soft, 0.1-1 keV, X-ray radiation from comets in the inner heliosphere. 3). Impacts of comets with the Sun with velocities more than 600 km/s will be accompanied by photospheric solar flares // IAU 28th GA, Scientific Session JD5: From meteors and meteorites to their parent bodies: Current status and future developments.