Gismondine, amicite, garronite, and gobbinsite-zeolites with the same structure type of the double-connected 4-ring chain group-were synthesized by long-term hydrothermal treatment of synthetic water-free glasses of the same compositions as the respective zeolite phases, in a temperature range between 200 and 250 degrees C at 1 kbar H2O pressure. Gismondine was formed from glass of the composition 4CaO-4Al(2)O(3)-8SiO(2) with tetragonal symmetry, and the preparation conditions could be successfully applied to the synthesis of zeolites amicite (monoclinic, glass composition 2Na(2)O-2K(2)O-4Al(2)O(3)-8SiO(2)), garronite (tetragonal, glass composition Na2O-2.5CaO-3Al(2)O(3)-10SiO(2)) and gobbinsite (tetragonal, glass composition 5Na(2)O-5Al(2)O(3)-22SiO(2)). The formation of these zeolite phases under the chosen p-T-t conditions was only dependent on the chemical composition of the glassy starting product. This behavior could be explained by a supersaturation-crystallization process, which, in principle, is applicable to synthesis of this class of materials.