The equations for a density matrix were used to calculate the radiation absorption of an arbitrary spectral composition and angular distribution. The calculation takes into consideration the saturation effect, the interaction of the absorbing molecues with the surroundings being described by means of the probabilities of non-optical transitions and not by means of approximate relaxation terms. The result are expressions for the absorption coefficient, taking into consideration its dependence on the intensity, spectral composition, direction of propagation and polarization of the radiation, which is absorbed in the region of one and the same absorption curve of the molecule. The relations also contain the dependence of the absorption coefficient on the intensity of the radiation absorbed in the region of other natural frequencies of the molecule and on all the probabilities of non-optical and spontaneous transitions.