For the gallium metals, a model is proposed that explains the mechanism of an anomalous increase in the differential capacitance of the EDL dense part of the metal-electrolyte interface at limiting anodic and cathodic polarizations. The considerable increase in the capacitance is explained by the resonance interaction between electronic states of the metal and the adjacent layer of solvent molecules. The potential dependence of the capacitance is interpreted in terms of the Breit-Wigner parameters of a resonant scattering.