Formation and properties of viscoelastic wormlike aqueous micellar solutions of the zwitterionic surfactant p-dodecyloxybenzyldimethylamine oxide (pDoAO) were studied. Semi-dilute aqueous solutions of pDoAO show a sharp increase in viscosity, which exceeds 160 cST for concentrations >50 mM, leading to viscoelastic solutions. Viscoelasticity relates to the surfactant charge type. In fact this viscoelastic system reverses to fluid when acid is added (pH<2), which changes the system to cationic. Under acidic conditions the system resembles solutions of the similar cationic surfactant p-dodecyloxybenzyltrimethylammonium bromide, (pDoTABr) in terms of viscosity. Properties of aqueous solutions of pDoAO were investigated by dynamic light scattering (DLS), rheology and small angle neutron scattering (SANS). Data support the idea that small micelles grow in length (wormlike or threadlike micelles) as surfactant concentration increases and viscoelastic solutions form as micelles become entangled. The micellar diameter as calculated by different techniques is about 5 nm.