Folding-up system intended to fold an end section (3A, 3B) of a cylindrical wall of a tyre carcass assembly around a reinforcing bead core (4, 5) of said carcass assembly, said cylindrical wall extending along and around a central axis called the "roll axis", and said reinforcing bead core (4, 5) extending along a generatrix (L4, L5) forming a ring around said roll axis, said system comprising: - a folding device, comprising at least one pressing member (11, 12, 13) such as a pressure roller (11, 12, 13), and arranged to cause said pressing member (11, 12, 13) to be applied against the radially outer face (3A_out, 3B_out) of the end section (3A, 3B), in an angular sector (A11, A12, A13) of the cylindrical wall called the "angular working sector" (A11, A12, A13) which corresponds to a fraction of the circumference of the end section (3A, 3B) around the roll axis, and to cause said pressing member to execute a tilting pitching movement about the generatrix (L4, L5) of the reinforcing bead core (4, 5), so that the pressing member (11, 12, 13) folds the portion of the end section (3A, 3B) located in the angular working sector (A11, A12, A13) concerned towards the radially inner face (3_in) of the cylindrical wall of the carcass assembly, around the reinforcing bead core (4, 5), said system being characterized in that it comprises: - a drive device designed to modify the relative position of the pressing member (11, 12, 13), by successive angular increments, with respect to the carcass assembly about the roll axis, so that the pressing member (11, 12, 13) can execute its tilting pitching movement in different angular working sectors (A11, A12, A13) in order to fold the corresponding portions of the end section (3A, 3B) one after another, - a selector designed to place the pressing member (11, 12, 13), alternately, in a working configuration, enabling said pressing member (11, 12, 13) to bear against the radially outer face (3A_out, 3B_out) of the end portion in the angular working sector (A11, A12, A13) concerned and to force the corresponding portion of the end section (3A, 3B) to be folded when the folding device executes the tilting pitching movement in said angular working sector (A11, A12, A13) concerned, and then in a withdrawn configuration which prevents said pressing member (11, 12, 13) from interfering with the end section (3A, 3B) when the drive device modifies the relative position of said pressing member (11, 12, 13) with respect to the cylindrical wall of the carcass assembly, about the roll axis, to change the angular working sector. - a folding device, comprising at least one pressing member (11, 12, 13) such as a pressure roller (11, 12, 13), and arranged to cause said pressing member (11, 12, 13) to be applied against the radially outer face (3A_out, 3B_out) of the end section (3A, 3B), in an angular sector (A11, A12, A13) of the cylindrical wall called the "angular working sector" (A11, A12, A13) which corresponds to a fraction of the circumference of the end section (3A, 3B) around the roll axis, and to cause said pressing member to execute a tilting pitching movement about the generatrix (L4, L5) of the reinforcing bead core (4, 5), so that the pressing member (11, 12, 13) folds the portion of the end section (3A, 3B) located in the angular working sector (A11, A12, A13) concerned towards the radially inner face (3_in) of the cylindrical wall of the carcass assembly, around the reinforcing bead core (4, 5), said system being characterized in that it comprises: - a drive device designed to modify the relative position of the pressing member (11, 12, 13), by successive angular increments, with respect to the carcass assembly about the roll axis, so that the pressing member (11, 12, 13) can execute its tilting pitching movement in different angular working sectors (A11, A12, A13) in order to fold the corresponding portions of the end section (3A, 3B) one after another, - a selector designed to place the pressing member (11, 12, 13), alternately, in a working configuration, enabling said pressing member (11, 12, 13) to bear against the radially outer face (3A_out, 3B_out) of the end portion in the angular working sector (A11, A12, A13) concerned and to force the corresponding portion of the end section (3A, 3B) to be folded when the folding device executes the tilting pitching movement in said angular working sector (A11, A12, A13) concerned, and then in a withdrawn configuration which prevents said pressing member (11, 12, 13) from interfering with the end section (3A, 3B) when the drive device modifies the relative position of said pressing member (11, 12, 13) with respect to the cylindrical wall of the carcass assembly, about the roll axis, to change the angular working sector.