During recovery of an offshore pipeline, to a floating vessel for repair, for example, the pipeline is secured to a hang-off clamp. Due to the motion of the vessel, oscillating bending moments can be caused in the pipeline below the clamp. To reduce these bending moments an auxiliary member is employed which restricts "radial" movement of the pipeline below the clamp. The auxiliary member comprises an elongate element, such as a pipe, whose upper end is fixed to the vessel and whose lower end carries a member connecting it to the pipeline. Axial movement of the pipeline with respect to the connecting member is permitted. The auxiliary member is designed to have predetermined amount of flexibility, this being provided in particular by flexibility of the pipe, and it thus restricts the amount of radial movement of the pipeline which is permitted below the clamp.