A thrust reverser system includes a thrust reversal cascade and a reverser door which are accommodated in a housing situated outside a secondary flow duct. The system also includes connection parts the presence of which combined with the action of the actuator gives rise simultaneously to: displacement rearwards of the cascade in the direction of a nacelle opening, cleared by a nacelle cowling entrained rearwards together with the cascade; and a combined movement of the reverser door relative to the cascade, leading to displacement of the front end of the door rearwards along the cascade, and to pivoting of this door, such as to give rise to plunging of its rear end into the secondary flow duct.