Bending-active elastica beams represent structural members which are initially installed as straight beams and then bent into arched shapes by applying horizontal displacements to one support. Designing such members for permanent structures made of fiber-polymer composites involves complex viscoelastic responses, which have not yet been thoroughly investigated. An experimental investigation of medium-scale bending-active elastica beams, consisting of pultruded glass fiber-polymer composite profiles, was thus conducted to investigate the long-term structural behavior of such members under imposed sustained bending and axial compression. The results revealed that viscoelastic responses are based on an interaction of stress relaxation and creep with their effects increased with increasing bending degree and time of exposure to sustained strains and stresses. The imposed horizontal displacement to one of the supports to maintain the bent beam shape induced sustained bending stresses in the beam. Beneficial relaxation of these stresses occurred with relaxation predicted to reach 12 % during a targeted 50-year design service life. Furthermore, the likelihood of the curved beam exhibiting in-plane deformations under sustained stresses enabled creep to occur simultaneously, with associated in-plane creep deformations and strength reduction. While creep deformations remained insignificant, progressive creep rupture occurred at highest bending degrees, exhibiting sequential creep rupture in the outer combined mat layers, delamination, crack opening and final fiber failure. Creep rupture can be prevented by postponing crack initiation in the combined mat layer beyond the targeted design service life. This can be achieved by limiting the bending degree to 50 % of the bending degree at which short-term crack initiation occurs.