— Small-angle neutron scattering data on aqueous solutions of wormlike micelles of an anionic surfactant of potassium oleate in the presence of low molecular weight salt KCl have been studied for a wide range of surfactant concentrations. It is shown that, as the concentration of micelles in the network increases, the scattering intensity decreases because of the structure factor for small scattering vectors. The parameters of the local structure of micelles, which are independent of the surfactant concentration, are determined in the range of medium values of the scattering vectors. The values of the persistence length of wormlike micelles are obtained for small concentrations of potassium oleate. The correct persistence length of the micelles is found upon extrapolating the obtained values to the zero surfactant concentration, where there is no interaction between the micelles.