A cascade thrust reverser for an airplane dual flow jet engine nacelle is provided that includes a front frame holding a plurality of cascades, a cowling slidably mounted between a direct jet position and a reverse jet position. The cowl includes a substantially annular diaphragm that is placed edge-to-edge with the front frame and radially inside said cascades when said cowl is located in the direct jet position. Thrust reversal flaps are pivotably mounted onto the diaphragm, and cylinders for actuating the cowl are also provided. Upstream ends of the cylinders are mounted on a stationary portion of the nacelle, and the downstream ends of the cylinders are mounted on an upstream edge of the diaphragm.