A complex of scientific and technical problems directly related to the priority of ensuring the operational safety and reliability of the cores of promising power nuclear reactors with supercritical thermodynamic parameters of a light-water coolant is systematized. The problems of implementation of effective heat removal from the surface of fuel elements and ensuring reliable calculation of thermal and hydrodynamic processes in turbulent flows of a supercritical coolant are considered. The main attention in the consideration of thermohydraulic processes in the near-critical region is paid to the conditionality of the physical nature of these processes by the regularities of transformation of the thermophysical properties of the coolant with changes in its temperature. It is noted that these phenomena have not been sufficiently studied and that modern designers of nuclear reactors with supercritical parameters practically do not have physically substantiated adequate ideas about the physical nature of an emergency mode of deteriorated heat transfer, which can arise unpredictably on the surface of a fuel element even if it is continuously cooled by a coolant with supercritical parameters. It is only known that the main physical sign of the occurrence of this emergency mode is a significant deterioration in heat transfer, which becomes abnormally low, but the physical reasons for such a dangerous anomaly are currently unknown. Based on the analysis of the molecular kinetics data of the near-wall coolant layer, it was proposed to consider such facts of an emergency decrease in the heat transfer intensity due to the appearance of an unknown pseudo-film boiling regime on the fuel element surface. In this context, it is shown that under the conditions under study, macromolecular assemblies in the form of pseudo-vapor formations can appear on the heat exchange surface, as a result of which the heat transfer on the fuel element surface is disturbed. Using experimental data, it is shown that there is a rather deep physical analogy between heat transfer in a supercritical thermodynamic system and the subcooled boiling process at subcritical parameters of the coolant. The dynamics of changes in the characteristics of the experimental spectra of acoustic emission of pseudo-boiling with a sequential increase in the thermal load is analyzed and it is shown that these phenomena can, in principle, be used in promising systems for diagnostic monitoring of reactors with supercritical parameters for early detection of the initial phases of pseudo-boiling and prompt prevention of the occurrence of emergency modes of deteriorated heat transfer