A thrust reverser for a turbojet engine nacelle includes movable cowls which move backward relative to a front frame under the action of an actuation system, thereby making flaps tilt, via a control mechanism, so as to substantially close the annular cold air flow path, and by opening cascades disposed around this flow path and which receive the cold air flow and return it forward. When the thrust reverser is closed, the cascades are partially integrated in the cowls, and the thrust reverser includes an actuation system which makes the cascades move backward along a stroke which is shorter than the stroke of the cowl.