A device for joining the two stages 2 and 3 of a self-propelled engine comprises means for achieving the separation of the two stages 2 and 3 after the combustion of the pyrotechnic charge 12 of the rear stage 2 is completed, means for carrying out the ignition of the pyrotechnic charge 19 of the front stage 3.A rear part of the front stage 3 and a front part of the rear stage 2 are assembled together for sliding axial movement therebetween. A temporary connection breakable under the effect of the ignition of the rear stage 2 maintains a predetermined spacing e between the two stages. The front stage 3 includes means 22 and 23 for igniting, after a predetermined delay, a pyrotechnic charge 19 of the front stage 3 and the rear stage 2 includes means 29 for triggering the igniting means after said temporary connection is eliminated.