The perturbation of the rotational equilibrium caused by spontaneous and stimulated emission and the cooling of a molecular gas in the rotational band of diatomic molecules are studied theoretically_ It is shown that, in the case of a rarefied gas. spontaneous radiative rotational transitions of molecules influence the rotational distribution function and hence the cooling rate itself. Vibrational relaxation in gases is now well known, and its role in various physical and chemical phenomena and its basic features have been firmly established. Rotational relaxation has been discussed less frequent-ly_ In ref. [ 11, distortion of the rotational equilibrium under the influence of sources of rotationally excited particles and also relaxation of the primordial nonequilibrium distribution function have been studied theoretically (the gas itself does not radiate). This paper considers a perturbation of the rotationequilibrium caused by spontaneous and stimulated emission and the cooling of a rarefied gas in the rotational band of diatomic molecules. A non-equilibrium of this nature must be taken into consideration when deciphering molecular spectra of such non-equilibrum gas systems as the upper atmosphere, dark interstellar clouds and reactive gases. Another relevant problem is the calculation of the thermal balance in the upper atmosphere and in interstellar clouds. To do this, one has to define the nonequilibrium distribution function. This study is an attempt to calculate theoretically the cooling rate of a molecular gas by its emission in the rotational band. In the case of a rarefied gas, spontaneous radiative rotational transitions of molecules influence the rotational distribution function and hence the cooling rate itself.