The 22-carbon-tailed zwitterionic surfactant erucyl dimethyl amidopropyl betaine (EDAB) forms highly viscoelastic fluids in water at low concentrations and without the need for salt or other additives. Here, semidilute aqueous solutions of EDAB are studied by using a combination of rheological techniques, small-angle neutron scattering (SANS) and cryo-transmission electron microscopy (cryo-TEM). EDAB samples show interesting rheology as a function of temperature. At low temperatures (∼25 °C), a 50 mM EDAB sample behaves like an elastic gel with an infinite relaxation time and viscosity. Upon heating to ∼60 °C, however, the sample begins to respond like a viscoelastic solution; that is, the relaxation time and zero-shear viscosity become finite, and the rheology approaches that of a Maxwell fluid. The same pattern of behavior is repeated at higher EDAB concentrations. Cryo-TEM and SANS reveal the presence of giant wormlike micelles in all EDAB samples at room temperature. The results imply that, depending on temperature, EDAB wormlike micelles can exhibit either a gel-like response or the classical viscoelastic ("Maxwellian") response. The unusual gel-like behavior of EDAB micelles at low temperatures is postulated to be the result of very long micellar breaking times, which, in turn, may be due to the long hydrophobic tails of the surfactant.