Secured system for bagging objects in sealable security bags, suitable for being received in a security enclosure comprising side walls (7, 8), said system comprising a fixing structure in the enclosure, provided with means for receiving the sealable bag that can be displaced between a first position of holding the bag in an open position under an opening for the passage of the objects, formed in the fixing structure, and a second position of disengagement of the sealed bag relative to the fixing structure to allow it to be removed and replaced, the means for receiving the bag being provided with a first frame and a second frame, the first frame being mounted to slide relative to the second frame, characterised in that: - the fixing structure takes the form of a single-piece part of generally inverted U-shaped section, and the fixing structure is provided on its lateral edges (5, 6) with means (9, 10, 11, 12, 13, 14, 15, 16) for fixing by tightening between the side walls (7, 8) of the security enclosure, - the second frame is mounted to slide in the fixing structure, - roller bearing runners are interposed between the first and the second frames, - roller bearing runners are interposed between the second frame and the fixing structure, - the first frame comprises a front crossmember associated with a manoeuvring handle and a rear crossmember provided with means for attaching a first edge of the bag, - the second frame is provided with a front crossmember provided with means for attaching a second edge of the bag opposite the first, - the facing edges of the security bag comprise complementary contact sealing means, - the first frame is mounted to be displaceable by sliding relative to the second frame between a first position in which the rear crossmember of the first frame is separated from the front crossmember of the second frame to hold the bag open facing the opening for the passage of the objects formed in the fixing structure and a second position in which the rear crossmember of the first frame is pressed against the front crossmember of the second frame to bring the facing edges of the bag into contact with one another in order to effect sealing of the bag, - the second frame is mounted to be displaceable by sliding in the fixing structure between a first position of holding of the security bag in the fixing structure and a second position in which the first frame protrudes relative to the fixing structure to allow it to be removed and replaced, and - the system comprises means (31, 32) for controlling the relative displacements of the first frame relative to the second frame and of the second frame relative to the fixing structure, to allow the displacement of the first frame relative to the second frame before the displacement of the second frame relative to the fixing structure, in order to effect sealing of the bag before its disengagement from the fixing structure. - the fixing structure takes the form of a single-piece part of generally inverted U-shaped section, and the fixing structure is provided on its lateral edges (5, 6) with means (9, 10, 11, 12, 13, 14, 15, 16) for fixing by tightening between the side walls (7, 8) of the security enclosure, - the second frame is mounted to slide in the fixing structure, - roller bearing runners are interposed between the first and the second frames, - roller bearing runners are interposed between the second frame and the fixing structure, - the first frame comprises a front crossmember associated with a manoeuvring handle and a rear crossmember provided with means for attaching a first edge of the bag, - the second frame is provided with a front crossmember provided with means for attaching a second edge of the bag opposite the first, - the facing edges of the security bag comprise complementary contact sealing means, - the first frame is mounted to be displaceable by sliding relative to the second frame between a first position in which the rear crossmember of the first frame is separated from the front crossmember of the second frame to hold the bag open facing the opening for the passage of the objects formed in the fixing structure and a second position in which the rear crossmember of the first frame is pressed against the front crossmember of the second frame to bring the facing edges of the bag into contact with one another in order to effect sealing of the bag, - the second frame is mounted to be displaceable by sliding in the fixing structure between a first position of holding of the security bag in the fixing structure and a second position in which the first frame protrudes relative to the fixing structure to allow it to be removed and replaced, and - the system comprises means (31, 32) for controlling the relative displacements of the first frame relative to the second frame and of the second frame relative to the fixing structure, to allow the displacement of the first frame relative to the second frame before the displacement of the second frame relative to the fixing structure, in order to effect sealing of the bag before its disengagement from the fixing structure.