A turbojet engine nacelle has a thrust reverser device and an actuating system for said thrust reverser device, and the thrust reverser device includes a moving cowl mounted translatably alternating between a closed position and an open position, and a jet nozzle section for gases that extends the moving cowl. In particular, the jet nozzle section includes a nozzle flap mounted movable between a closed position and an open position in which the nozzle flap opens a leakage passage toward the outside of the nozzle section. The actuating system has an actuator shared with the moving cowl and the nozzle flap to activate the translational movement of the moving cowl and to pivot the nozzle flap between three following positions: an idle position, an open position of the nozzle flap and an open position of the moving cowl.