We theoretically investigate the formation of photon-echo signals in a
gas under conditions when the velocities of gas particles are compara
ble with the speed of light. Relativistic corrections to spatial phase
-matching conditions and the moment of generation of an echo response
in the time domain are derived for the signals of stimulated and phase
-conjugate photon echo. The specific features of echo-hologram recordi
ng on a flow of relativistic particles are considered.