A thrust reverser for a nacelle of a turbojet engine includes deflecting cascades and an external cowl which translates from a closure position to an opening position by a set of control cylinders being attached by their ends to the external cowl. The deflecting cascades are supported by a front frame and a rear frame respectively and are enclosed in an envelope formed by a fan carter and by a fan cowl. The thrust reverser further includes a lock which is able to connect or disconnect the deflecting cascades to the external cowl. When the lock is unlocked, the set of control cylinders translate the external cowl alone in downstream direction while in the lock position, the control cylinders translates the external cowl and the deflecting cascades together in downstream direction.