Apparatus for selectively cross-folding sequentially printed sheets (2, 3) following one another, comprising • a first transport segment, on which printed sheets (2, 3) transported one after another in a guide plane are providable in a folding position, • at least two folding rolls, which are arranged on a first side of the guide plane, each have an axis of rotation and form between them a folding gap for first printed sheets to be cross-folded, and the axes of rotation of which are aligned both substantially parallel to each other and also substantially parallel to the guide plane, • a compressed air device which is oriented substantially parallel to the axes of rotation of the folding rolls, is arranged on a second side of the guide plane, opposite the first side of the guide plane, and is arranged in the region of the folding gap, which is connected to a compressed air source and to a control unit and has at least one outlet opening for compressed air that is directed at the folding gap, • a second transport segment for cross-folded first printed sheets and a third transport segment for unfolded second printed sheets, wherein the first, second and third transport segments (5, 28, 32) have a common first segment point, at which the first transport segment ends and both the second transport segment and the third transport segment begin, and wherein the common first segment point is located on a line of intersection of the guide plane and a folding plane extending through the folding gap and the at least one outlet opening of the compressed air device, wherein • the compressed air device has a first control element connected to the control unit for selectively triggering or suppressing a compressed air blast from the at least one outlet opening of the compressed air device in such a way that, in each case starting from the folding position, a first printed sheet is introductable into the second transport segment to be folded or a second printed sheet is introductable into the third transport segment to bypass the folding, characterized in that • the third transport segment opens into the second transport segment downstream of the folding rolls at a common second segment point, • a fourth transport segment follows downstream of the common second segment point, and • the third transport segment is longer than the second transport segment or is operable more slowly than the second transport segment in such a way that a first sequence of the printed sheets (2, 3) following one another on the first transport segment is the same as a second sequence of the printed sheets (2, 3) following one another on the fourth transport segment. • a first transport segment, on which printed sheets (2, 3) transported one after another in a guide plane are providable in a folding position, • at least two folding rolls, which are arranged on a first side of the guide plane, each have an axis of rotation and form between them a folding gap for first printed sheets to be cross-folded, and the axes of rotation of which are aligned both substantially parallel to each other and also substantially parallel to the guide plane, • a compressed air device which is oriented substantially parallel to the axes of rotation of the folding rolls, is arranged on a second side of the guide plane, opposite the first side of the guide plane, and is arranged in the region of the folding gap, which is connected to a compressed air source and to a control unit and has at least one outlet opening for compressed air that is directed at the folding gap, • a second transport segment for cross-folded first printed sheets and a third transport segment for unfolded second printed sheets, wherein the first, second and third transport segments (5, 28, 32) have a common first segment point, at which the first transport segment ends and both the second transport segment and the third transport segment begin, and wherein the common first segment point is located on a line of intersection of the guide plane and a folding plane extending through the folding gap and the at least one outlet opening of the compressed air device, wherein • the compressed air device has a first control element connected to the control unit for selectively triggering or suppressing a compressed air blast from the at least one outlet opening of the compressed air device in such a way that, in each case starting from the folding position, a first printed sheet is introductable into the second transport segment to be folded or a second printed sheet is introductable into the third transport segment to bypass the folding, characterized in that • the third transport segment opens into the second transport segment downstream of the folding rolls at a common second segment point, • a fourth transport segment follows downstream of the common second segment point, and • the third transport segment is longer than the second transport segment or is operable more slowly than the second transport segment in such a way that a first sequence of the printed sheets (2, 3) following one another on the first transport segment is the same as a second sequence of the printed sheets (2, 3) following one another on the fourth transport segment.