[en] The strictly reversible, thermodynamically equilibrium nature of the free rotation of a body makes it possible to obtain a number of bounds on the rotational characteristics within individual rotational bands of nonspherical nuclei. As a result, the bounds between which the possible values of the critical spin J/sub C/ lie can be expressed exclusively in terms of a restricted number of the experimentally most accessible data on the lower phase J< J/sub C/ for a given nuclide. The bounds are tested on the ground-state rotational bands (yrast lines) of even--even nuclei, in which the corresponding phase transition (backbending) has already been observed experimentally. For nuclei with pronounced nonsphericity, all the bonds are invariably confirmed. For the ground-state rotational bands for which the phase transition point J = J/sub C/ has not yet been reached, predictions are made for the corresponding values of J/sup min//sub C/ and, especially, J/sup max//sub C/. The specific features of excited rotational bands, and also the bands of odd nuclei are discussed