A theory is developed for the modified tri-level photon echo formed in gaseous media. Consideration is given to the cases when echo is generated both by atoms for molecules with zero nuclear spin and by atoms with non-zero nuclear spin. In the first case, it is shown that this particular kind of photon echo can be used to measure the relaxation characteristics of the multipole moments of the optically forbidden transition. On the basis of these considerations new experiments are suggested for the observation of the relaxation characteristics mentioned above. In the second case, formulae are obtained for the calculation of pre-exponential factors describing the dependence of the quantum beats of the intensity of the modified tri-level photon echo as a function of the time intervals between the exciting pulses. Values of the pre-exponential factors need to be known in order to correctly obtain spectroscopic information about an optically forbidden transition.