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A method of determining the relaxation constants of the multipole moments of gas atoms with non-zero nuclear spin has been proposed by using the polarisation properties and damping law of the non-stationary Raman scattering (NRS) of light. Correct account was taken of the depolarising atomic collisions and of the effect of the hyperfine structure (HFS) of the atomic levels. The NRS polarisation properties found have been assumed to be a basis method for the identification of optically forbidden transitions in both the electronic and total angular momenta. A possible method of determining the HFS constants through analysis of the NRS quantum beats has been established.