A thrust reverser system includes two thrust reversal cascades, of which the first cascade is entrained by an actuator, and which are configured to adopt a retracted position in which they are housed in a space located outside the duct. The action of the actuator brings about: rearward displacement of the first cascade in the direction of a nacelle opening; and during part of the rearward displacement of the second cascade, simultaneous pivoting of this second cascade under the action of a control lever, the interaction of which with a fixed guide rail forces the front end of the lever to move radially inwards while the lever is entrained rearwards by the second cascade.