Rheological investigations of viscoelastic surfactant solutions, both theoretical and experimental, have primarily focused on anionic or cationic surfactant molecules and charged counterion pairs. In this article, we present an experimental investigation on the linear flow properties (stress relaxation) of uncharged aqueous dimer acid betaine solutions as a function of surfactant and salt concentration. In the zwitterionic dimer acid betaine solutions, the electrostatic interactions among the surfactant molecules are primarily not screened by counterions. As a consequence, the theological properties are different from charged monomeric surfactant solutions. The analysis of the theological properties of dimer acid betaine reveals that this surfactant system behaves differently from anionic or cationic compounds. Dimer acid betaine solutions with and without salt do not show monoexponential relaxation phenomena that are typical for kinetically controlled relaxation mechanisms. Introducing NaCl also leads to gel forming and an even higher stability of the aggregates. As a conclusion, the theological properties such as the zero shear viscosity, relaxation times, of relaxation moduli are mainly controlled by diffusion (reptation) processes. A model for the linear stress decay developed for ionic surfactants was used to characterize basic structural parameters. The aggregation of the surfactant and the structure of the supramolecular aggregates are, however, not completely decoded by the used model showing the complex nature of zwitterionic dimeric surfactant systems.