[en] In the framework of the thermodynamic approach a number of inequalities are derived which restrict the rotational characteristics in separate rotational bands of nonspherical even-even nuclei. It is shown that the lower and upper limits between which possible values of the critical spin Jsub(C) lie can be expressed exclusively in terms of a restricted number of the most experimentally accessible data on the lower phase J< Jsub(C) for a given nuclide. A verification is performed for the ground state rotational bands (yrast-lines) of even-even nuclei in which the corresponding phase transition (backbending) has already been observed experimentally. For pronouncedly nonspherical nuclei all of the inequalities are invariably confirmed. For those of the ground state rotational bands for which the phase transition point J=Jsub(C) has not been attained experimentally, predictions are maid in relation to the values of their Jsub(C)sup(min) and in particular of Jsub(C)sup(max). The characteristic features of excited rotational bands and of the bands of odd nuclei are discussed