Nanoporous materials have important industrial applications as molecular sieves, catalysts and in gas separation and storage. They are normally produced as moderately dense silicates (SiO2) and aluminosilicates making their specific capacities for the uptake and storage of gases, such as hydrogen, relatively low. Here we report the synthesis and characterization of lightweight, nanoporous structures formed from the metal hydroxide Be(OH)2 in combination with relatively low levels of framework phosphate or arsenate. Three new zeotype structures are described, constructed mainly of Be(OH)4 tetrahedra bridged through hydroxide into three-membered rings; these units link together to produce several previously unknown zeotype cage types and some of the most structurally complex, nanoporous materials ever discovered. These materials have very low densities between 1.12 and 1.37 g cm−3 and theoretical porosities of 63–68% of their total volume thereby yielding very high total specific pore volumes of up to 0.60 cm3 g−1.