A method of determining the relaxation rates of the electronic and electronic nuclear multipole moments of gas atoms with non-zero nuclear spin using the Stokes three-level echo (STE) and the photon echo (PE) has been proposed. This method utilises the polarisation properties and damping laws of the STE and PE on the inhomogeneously broadened transitions. Correct account was taken of the hyperfine structure (HFS) of the atomic levels and of the effect of the depolarising atomic collisions. The STE polarisation properties found have also been assumed to be a basis method for the identification of optically forbidden transitions in total angular momentum.