An apparatus for guiding an oscillating or reciprocating continuous casting mold at a continuous casting installation having a curved axis of the path of travel of the strand, by means of a hinge or linkage mechanism equipped with at least four elements, wherein one element with a respective hinge at the ends thereof is formed by a mold arrangement which may be the mold itself or the mold and an extension thereof and another element serving as a frame is formed by a part of the structure of the installation. The paths of movement of the hinges are curved at the mold opposite to the axis of the path of travel of the strand.
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