Arrangement for supporting a tension member, in particular a stay cable or a tendon, transversely with respect to a longitudinal extent direction thereof in the region of a structure which is close to the anchorage, - comprising a cavity pipe which receives the tension member in the region close to the anchorage and extends coaxially along a first longitudinal axis, one end of said cavity pipe having a first axially loadable bearing surface that is concentric with respect to the first longitudinal axis, characterised by an adapter ring which has a first axially loadable support surface on its first side facing the cavity pipe, which bearing surface extends concentrically with respect to the first longitudinal axis and is designed for mounting the adapter ring in a predetermined position on the first bearing surface of the cavity pipe after rotation about the first longitudinal axis, and - which has a second axially loadable bearing surface on its second side facing away from the cavity pipe, which bearing surface extends concentrically with respect to a second longitudinal axis and has an eccentricity E 1 with respect to the first longitudinal axis, - a tubular or annular supporting element that has a second axially loadable support surface which is arranged concentrically with respect to the second axially loadable bearing surface of the adapter ring and the opening in which, which encircles a third longitudinal axis, forms a supporting surface for the tension member by means of its inner circumference, the opening having an eccentricity E 2 with respect to the second axially loadable support surface of the supporting element, - fastening means (37, 38) for axially clamping the cavity pipe, the adapter ring and the supporting element in their position relative to one another. - comprising a cavity pipe which receives the tension member in the region close to the anchorage and extends coaxially along a first longitudinal axis, one end of said cavity pipe having a first axially loadable bearing surface that is concentric with respect to the first longitudinal axis, characterised by an adapter ring which has a first axially loadable support surface on its first side facing the cavity pipe, which bearing surface extends concentrically with respect to the first longitudinal axis and is designed for mounting the adapter ring in a predetermined position on the first bearing surface of the cavity pipe after rotation about the first longitudinal axis, and - which has a second axially loadable bearing surface on its second side facing away from the cavity pipe, which bearing surface extends concentrically with respect to a second longitudinal axis and has an eccentricity E 1 with respect to the first longitudinal axis, - a tubular or annular supporting element that has a second axially loadable support surface which is arranged concentrically with respect to the second axially loadable bearing surface of the adapter ring and the opening in which, which encircles a third longitudinal axis, forms a supporting surface for the tension member by means of its inner circumference, the opening having an eccentricity E 2 with respect to the second axially loadable support surface of the supporting element, - fastening means (37, 38) for axially clamping the cavity pipe, the adapter ring and the supporting element in their position relative to one another.