The existence of ultra-fl exible low-energy forms of boron oxides (B 2 O 3 and BO) is demonstrated, in particular structures in which B 3 O 3 or B 4 O 2 six-membered rings are linked by single B-O-B bridges. The minima in the energy landscapes are remarkably broad; the variation in the internal energies is very small over a very large range of volumes. Such volume changes may even exceed 200%. This remarkable behavior is attributed predominantly to the pronounced angular fl exibility of the B-O-B bridges linking the rings, which is unusual for a covalent bond. At larger volumes, the structures are nanoporous; the pores collapse upon compression with negligible change in energy, making these suitable as guest-host materials. In marked contrast, in other materials where low density frameworks have been reported or predicted, such low-density phases are considerably higher in energy. The fl exibility of the structures also offers a resolution of the long-standing controversy reconciling the structure and density of vitreous B 2 O 3 .