To investigate the interaction of surfactants with ions, we measured the conductance of aqueous solutions of sodium dodecyl sulphate (SDS) and lithium dodecyl sulfate (LDS) with added electrolytes NaCl, KCl, and LiCl as a function of the surfactant concentration and the electrolyte concentration. Measurements were carried out on a broadband dielectric spectrometer BDS-80, Novocontrol. Experiments cover a broad range of the surfactant and electrolyte concentrations, from above the critical micelle concentration (CMC) to infinite dilution. Experimental data are compared with predictions for the concentration dependence of electrical conductance provided by theories for strong electrolytes. We consider the classical Onsager-Fuoss equation for a binary electrolyte, the Onsager-Kim equation for a multicomponent electrolyte, and equations for a three-component electrolyte recently derived within the mean spherical approximation. Deviation of theoretical predictions for strong electrolytes from experimental data on surfactant solutions provides insight into the formation of micellar aggregates below the CMC point.