The remarkable stability of Archaebacteria and their resistance to extreme environmental conditions, such as high temperature (hot springs), high salinity (salt marsh), high acidity (volcanic environment), or low temperature (Arctic or Antarctic) is mostly due to their very stable membranes. Membranes of Archaebacteria are composed of tetraethers from the lipid family of bolaamphiphiles. The concern in our laboratory is to synthesize bolaamphiphiles that could form vectors with function to carry drugs toward target cells in the body. The new family of bolamphiphiles synthesized has one polar head based on a sugar moiety and the other polar head is glycine betaine, both issued from natural sources (sugar beet, wheat). They are interconnected with a hydrocarbon chain of 12 methylène units. One side hydrocarbon chain, of 8 methylène units is attached to the anomeric position of the sugar moiety. These two molecules are named N-(12-Betainylamino-Dodecane)-octyl β-D-Glucofuranosiduronamide Chloride, abbreviated C8C12 and N-(12-Betainylamino-Dodeca-5,7-diynyl)-octyl β-D-Glucofuranosiduronamide Chloride, abbreviated C8C12X2. These bolaamphiphile molecules organize in membrane-mimetic lamellar structures (Lc, Lα, L). They undergo a thermal phase transition upon heating. When cooled back to room temperature, they remain in the undercooled high-temperature phase. To follow the relaxation back to the thermodynamically stable phase at 20 °C, the small-angle and wide-angle X-ray spectra were recorded every hour. The Deborah number (De), defined as De = time of relaxation/time of observation, is a dimensionless number often used in rheology to characterize the fluidity of materials under specific flow conditions. It was evaluated for supramolecular structures of two type of bolaamphiphiles, as the De(C8C12) = 35 and the De(C8C12X2) = 62. These values are typical for solid-like behavior, which is in accordance with the sticky, paste-like, brownish aspect of these bolaamphiphile assemblies. The time of relaxation was the time for bolaamphiphiles to regain their thermodynamically stable phase at 20 °C and the time of observation was 1 h, the typical time of recording between two subsequent spectra.