A tenter-clip carriage for a stretching system, comprising the following features: - the tenter-clip carriage has a longitudinal direction and a transverse direction, a. wherein the longitudinal direction runs between a leading side and a trailing side opposite thereto; and b. wherein the transverse direction runs transversely or perpendicularly to the longitudinal direction between a clamping side, aligned laterally therewith, for a material web to be stretched and a guide rail side opposite thereto; - the tenter-clip carriage comprises a clip body, wherein the clip body has a clamping device via which a material web edge of a material web to be stretched can be clamped; - the tenter-clip carriage comprises fastening portions in order to fasten the tenter-clip carriage to a partial chain portion of a conveyor chain arrangement of the stretching system; - the tenter-clip carriage comprises at least one stabilising roller (19d, 19d', 19d") or at least one stabilising sliding element (19d, 19d', 19d"); characterised by the following features: - the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d") is, by means of a guide device: a) held directly on the tenter-clip carriage; or b) held indirectly on and/or connected to the tenter-clip carriage via a pin that connects two chain segments (11 1, 11 2) of the partial chain portion of the conveyor chain arrangement to one another; and, specifically, unaffected by the feed and drive forces acting on the tenter-clip carriage or the partial chain portion to move the tenter-clip carriage and/or the partial chain portion, and - the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d") can be adjusted perpendicularly or transversely to the longitudinal direction; - for the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d"), a force accumulator or spring-force accumulator is provided via which the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d") is held forcibly in a yieldable manner and/or held in a pretensioned manner with a predeterminable or presettable force away from the clamping side in the direction of the guide rail side opposite the tenter-clip carriage and/or opposite the partial chain portion of the conveyor chain arrangement. - the tenter-clip carriage has a longitudinal direction and a transverse direction, a. wherein the longitudinal direction runs between a leading side and a trailing side opposite thereto; and b. wherein the transverse direction runs transversely or perpendicularly to the longitudinal direction between a clamping side, aligned laterally therewith, for a material web to be stretched and a guide rail side opposite thereto; a. wherein the longitudinal direction runs between a leading side and a trailing side opposite thereto; and b. wherein the transverse direction runs transversely or perpendicularly to the longitudinal direction between a clamping side, aligned laterally therewith, for a material web to be stretched and a guide rail side opposite thereto; - the tenter-clip carriage comprises a clip body, wherein the clip body has a clamping device via which a material web edge of a material web to be stretched can be clamped; - the tenter-clip carriage comprises fastening portions in order to fasten the tenter-clip carriage to a partial chain portion of a conveyor chain arrangement of the stretching system; - the tenter-clip carriage comprises at least one stabilising roller (19d, 19d', 19d") or at least one stabilising sliding element (19d, 19d', 19d"); characterised by the following features: - the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d") is, by means of a guide device: a) held directly on the tenter-clip carriage; or b) held indirectly on and/or connected to the tenter-clip carriage via a pin that connects two chain segments (11 1, 11 2) of the partial chain portion of the conveyor chain arrangement to one another; and, specifically, unaffected by the feed and drive forces acting on the tenter-clip carriage or the partial chain portion to move the tenter-clip carriage and/or the partial chain portion, and a) held directly on the tenter-clip carriage; or b) held indirectly on and/or connected to the tenter-clip carriage via a pin that connects two chain segments (11 1, 11 2) of the partial chain portion of the conveyor chain arrangement to one another; - the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d") can be adjusted perpendicularly or transversely to the longitudinal direction; - for the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d"), a force accumulator or spring-force accumulator is provided via which the at least one stabilising roller (19d, 19d', 19d") or the at least one stabilising sliding element (19d, 19d', 19d") is held forcibly in a yieldable manner and/or held in a pretensioned manner with a predeterminable or presettable force away from the clamping side in the direction of the guide rail side opposite the tenter-clip carriage and/or opposite the partial chain portion of the conveyor chain arrangement.