Turbofan engine having a longitudinal direction and comprising an engine and a nacelle surrounding the engine which comprises a fan casing, in which a path of a bypass stream is delimited between the nacelle and the engine and in which an air stream circulates from front to rear of the turbofan engine, said nacelle comprising: - a fixed structure fixed to the fan casing, - a movable cowl which is movable in translation on the fixed structure in a direction of translation between an advanced position in which the movable cowl is positioned in such a way that it is close to the fan casing and a retracted position in which the movable cowl is positioned in such a way that it is away from the fan casing to define between them a window which is opened between the flow path and the outside of the nacelle, - a set of actuators ensuring the displacement of the movable cowl between the advanced position and the retracted position, and vice versa, - a plurality of flexible veils, having a first edge fixed to the movable cowl and a second edge opposite the first edge, in which said veil can alternately assume a folded position in which said veil is housed in the movable cowl or a deployed position in which said veil is extended between the first edge and the engine across the flow path, and characterized in that it comprises: - a pneumatic system arranged to displace the second edge of each veil in order to displace said veil from the folded position to the deployed position and to displace the second edge of each veil in order to displace said veil from the deployed position to the folded position, in which the pneumatic system comprises: - a rigid main roll fixed inside the movable cowl to the rear of the window, - for each veil, at least one extendable secondary roll secured to the main roll and in which the inside of each secondary roll is in fluidic continuity with the inside of the main roll, in which the second end of said veil is fixed to each of said secondary rolls, and - a pressurization and depressurization system which, alternately, generates a pressure in the main roll and therefore in each secondary roll to inflate them in the transition from the advanced position to the retracted position, or generates a depression in the main roll and therefore in each secondary roll to deflate them in the transition from the retracted position to the advanced position. - a fixed structure fixed to the fan casing, - a movable cowl which is movable in translation on the fixed structure in a direction of translation between an advanced position in which the movable cowl is positioned in such a way that it is close to the fan casing and a retracted position in which the movable cowl is positioned in such a way that it is away from the fan casing to define between them a window which is opened between the flow path and the outside of the nacelle, - a set of actuators ensuring the displacement of the movable cowl between the advanced position and the retracted position, and vice versa, - a plurality of flexible veils, having a first edge fixed to the movable cowl and a second edge opposite the first edge, in which said veil can alternately assume a folded position in which said veil is housed in the movable cowl or a deployed position in which said veil is extended between the first edge and the engine across the flow path, and characterized in that it comprises: - a pneumatic system arranged to displace the second edge of each veil in order to displace said veil from the folded position to the deployed position and to displace the second edge of each veil in order to displace said veil from the deployed position to the folded position, in which the pneumatic system comprises: - a rigid main roll fixed inside the movable cowl to the rear of the window, - for each veil, at least one extendable secondary roll secured to the main roll and in which the inside of each secondary roll is in fluidic continuity with the inside of the main roll, in which the second end of said veil is fixed to each of said secondary rolls, and - a pressurization and depressurization system which, alternately, generates a pressure in the main roll and therefore in each secondary roll to inflate them in the transition from the advanced position to the retracted position, or generates a depression in the main roll and therefore in each secondary roll to deflate them in the transition from the retracted position to the advanced position.