The Raman photon echo (RPE) in atomic vapour, allowing for depolarising atomic collisions and hyperfine structure of the atomic levels, has been studied theoretically. A new method of determining the electronic and electronic nuclear relaxation rates of the multipole moments of gas atoms with non-zero nuclear spin using the RPE has been proposed. The RPE method also makes it possible to measure the derivatives of these relaxation rates with respect to the impurity gas pressure. A method of determining the energy separation between the hyperfine structure sublevels has been developed. This method is based on the quantum beats of the RPE intensity and may be used when the hyperfine splitting is less than the Doppler linewidth. A possibility of identifying the forbidden transitions in both the electronic and total angular momenta has been shown.