The behavior of a star with a thermonuclear energy source consistent with our present knowledge about nuclear reactions is studied in relation to the problems of stellar evolution and interpretation of the Hertzsprung-Russell diagram and mass-luminosity relation. It is found that in the case of ordinary thermonuclear reactions, with the absence of selective temperature effects (nuclear resonance) the central temperature and luminosity of the star (with constant mass) will rapidly increase in the process of evolution. If, however, such selective effects are present, the energy-production at the center of the star will cease, beginning with the stage when the central temperature reaches the selective value, and energy will be produced only in a spherical shell around the center. This shell will have exactly the selective temperature value corresponding to the thermonuclear reaction in question, and its radius will slowly increase in the process of evolution causing a very slow increase of luminosity. Finally, in the third stage of evolution, when all hydrogen necessary for thermonuclear reactions has been consumed, the star will start a rapid contraction and, passing through the high density stage, will end its life as a cool body. It is also indicated that the star model with a shell source does not possess the property of "super-stability" characteristic for the point-source models.