Spectral induced polarization or complex conductivity is a promising electric method in hydrogeophysics because of its sensitivity to water saturation, permeability, and particle size distribution (PSD). However, the physical and chemical mechanisms that generate the low-frequency complex conductivity of clays are still debated. To explain these mechanisms, the complex conductivity of kaolinite, smectite, and clay-sand mixtures was measured in the frequency range 1.4 mHz–12 kHz with various clay contents (100%, 20%, 5%, and 1% in volume of the clay-sand mixture) and salinities (distilled water, $0.1\mathrm{g}{\mathrm{L}}^{-1}$, $1\mathrm{g}{\mathrm{L}}^{-1}$, and $10\mathrm{g}{\mathrm{L}}^{-1}$ of NaCl in solution). The results indicated the strong impact of the cation exchange capacity of smectite upon the complex conductivity of the material. The quadrature conductivity increased steadily with the clay content and was fairly independent of the pore fluid salinity. A mechanistic induced polarization model was also developed. It combined a Donnan equilibrium model of the surface electrochemical properties of clays and sand, a conduction model of the Stern and diffuse layers, a polarization model of the Stern layer, and a macroscopic conductivity model based on the differential effective medium theory. It also included the effect of the PSD. Our complex conductivity model predicted very well the experimental data, except for very low frequencies ($<0.1\mathrm{Hz}$) at which membrane polarization may dominate the observed response.