A sewing system for sewing seams which lie multi-dimensionally in space - having a sewing head -- having a needle-bar upper part in which a needle bar is mounted so as to be driven in an upward and downward manner along the longitudinal axis of the latter, at least one sewing needle (9, 10) being held as a stitch-formation tool on said needle bar; -- having a sewing-head upper part in which the needle-bar upper part is mounted so as to be pivotable in a driven manner about the longitudinal axis of the needle bar; -- having a gripper lower part on which at least one gripper (15, 16) is mounted as a stitch-formation tool that is driven in a manner synchronous with the sewing needle (9, 10); -- having a sewing-head lower part in which the gripper lower part is mounted so as to be pivotable in a driven manner, and in a manner synchronous with the needle-bar upper part, about the longitudinal axis of the needle bar; - wherein motor components (19, 69) -- for driving the upward and downward movement of the needle bar, -- for pivoting the needle-bar upper part, -- for driving the gripper (15, 16) in a manner synchronous with the needle bar, -- for pivoting the gripper lower part - are disposed outside the needle-bar upper part and outside the gripper lower part and thus are not pivoted when the needle-bar upper part and the gripper lower part are pivoted. characterized in that the needle-bar upper part by way of at least one tongue-and-groove connection, having an annular member having a groove or a tongue, is operatively connected to a motor component for driving the upward and downward movement of the needle bar, wherein an axis of annular symmetry of the annular member coincides with the needle-bar longitudinal axis or is parallel with the latter. - having a sewing head -- having a needle-bar upper part in which a needle bar is mounted so as to be driven in an upward and downward manner along the longitudinal axis of the latter, at least one sewing needle (9, 10) being held as a stitch-formation tool on said needle bar; -- having a sewing-head upper part in which the needle-bar upper part is mounted so as to be pivotable in a driven manner about the longitudinal axis of the needle bar; -- having a gripper lower part on which at least one gripper (15, 16) is mounted as a stitch-formation tool that is driven in a manner synchronous with the sewing needle (9, 10); -- having a sewing-head lower part in which the gripper lower part is mounted so as to be pivotable in a driven manner, and in a manner synchronous with the needle-bar upper part, about the longitudinal axis of the needle bar; -- having a needle-bar upper part in which a needle bar is mounted so as to be driven in an upward and downward manner along the longitudinal axis of the latter, at least one sewing needle (9, 10) being held as a stitch-formation tool on said needle bar; -- having a sewing-head upper part in which the needle-bar upper part is mounted so as to be pivotable in a driven manner about the longitudinal axis of the needle bar; -- having a gripper lower part on which at least one gripper (15, 16) is mounted as a stitch-formation tool that is driven in a manner synchronous with the sewing needle (9, 10); -- having a sewing-head lower part in which the gripper lower part is mounted so as to be pivotable in a driven manner, and in a manner synchronous with the needle-bar upper part, about the longitudinal axis of the needle bar; - wherein motor components (19, 69) -- for driving the upward and downward movement of the needle bar, -- for pivoting the needle-bar upper part, -- for driving the gripper (15, 16) in a manner synchronous with the needle bar, -- for pivoting the gripper lower part -- for driving the upward and downward movement of the needle bar, -- for pivoting the needle-bar upper part, -- for driving the gripper (15, 16) in a manner synchronous with the needle bar, -- for pivoting the gripper lower part - are disposed outside the needle-bar upper part and outside the gripper lower part and thus are not pivoted when the needle-bar upper part and the gripper lower part are pivoted.