A support structure (1) is provided comprising a plurality of curved surfaces A, B hingedly interconnected along their edges such as to provide effective deployment in two separate stages. Preferably, the structure has only two curved surfaces hingedly interconnected at a single non-planar hinge line. In FIG. 1(a), the two sheets A, B are coplanar in that they lie in the same horizontal plane, permitting the structure to be in a flat, first stage deployment position. In Figure (b), the structure is fully deployed in a second stage deployment position by bringing sheet A out of plane through some angle in relation to the position of sheet B, resulting in both sheets becoming curved. The structure has utility in various space-based as well as terrestrial reflective and absorbing applications, and bears definite advantage in terms of weight saving, high stiffness and well-defined surface precision.