A riser support system for use in a body of water comprises a buoyant and ballastable support structure and a plurality of substantially vertical and rigid risers each of which is attached to the inside of the support structure at a location below the center of buoyancy of the support structure and below the surface of the body of water. Usually, each riser passes through the inside of a single tube in the support structure. Typically, the riser support system is used to support a plurality of risers and their surface wellheads inside the hull of an offshore platform, usually in such a manner that the axial movement of the risers and support structure is independent of the axial movement of the hull.